BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//CERN//INDICO//EN
BEGIN:VEVENT
SUMMARY:Lengths of closed geodesics in a hyperbolic link complements in S^
3.
DTSTART;VALUE=DATE-TIME:20091126T103000Z
DTEND;VALUE=DATE-TIME:20091126T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-248@cern.ch
DESCRIPTION:Colin Adams and Alan Reid showed that the length of the short
est closed geodesic in a hyperbolic knot or link complemement in S^3 is bo
unced above by 7.171646... We will show that the length of an n^th shortes
t closed geodesic in a hyperbolic knot or link complement in S^3 is at-mos
t a logarithmic function of n.\n\nhttps://indico.tifr.res.in/indico/confer
enceDisplay.py?confId=248
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=248
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the eigenvalues of graphs: results and conjectures
DTSTART;VALUE=DATE-TIME:20091217T103000Z
DTEND;VALUE=DATE-TIME:20091217T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-308@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
308
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=308
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometry of binary hermitian forms
DTSTART;VALUE=DATE-TIME:20091231T103000Z
DTEND;VALUE=DATE-TIME:20091231T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-381@cern.ch
DESCRIPTION:In a remarkabale booklet `The sensual(quadratic) form'\, J.H.
Conway introduces an elegant approach to integral binary quadratic forms.
The main tool is a 3 valence tree which is in fact an SL_2(Z)-equivariant
retract of the 2-dimensional hyperbolic space. Let A be the ring of integ
ers of a quadratic imaginary extension of the field of rational numbers. T
he 3-dimensional hyperbolic space has a 2-dimensional\, GL_2(A)-invariant
retract. The retract is a CAT(0) complex. In this lecture I will explain h
ow the retract can be used to derive some results on hermitian binary form
s over the ring A. This is a joint work with Mladen Bestvina.\n\nhttps://i
ndico.tifr.res.in/indico/conferenceDisplay.py?confId=381
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=381
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dicritical Divisors and Jacobian Problem
DTSTART;VALUE=DATE-TIME:20100107T103000Z
DTEND;VALUE=DATE-TIME:20100107T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-387@cern.ch
DESCRIPTION:The dicritical divisor coming out of integrable holonomie in d
ynamical systems which belong to the domain of real analysis gets miraculo
usly married to the jacobian problem of algebraic geometry. This is a gods
end for making inroads into the fortress jacobian. It also provides a shar
p tool for studying local functions on algebraic as well as analytical sur
faces. Although the jacobian problem is restricted to zero characteristic\
, it is amazing that the dicriticals\, born out of real analysis\, throw l
ight on the theory of local rings of prime characteristic. We owe the real
and complex theory of\ndicriticals to the pioneers like Artal\, Cassou-No
gues\, Eisenbud\, Fourrier\, Mattei\, Moussu\, Neumann\, Norbury and Rudol
ph. .........(continue)\n\nhttps://indico.tifr.res.in/indico/conferenceDis
play.py?confId=387
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=387
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cohomology theory for topological groups
DTSTART;VALUE=DATE-TIME:20100114T103000Z
DTEND;VALUE=DATE-TIME:20100114T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-403@cern.ch
DESCRIPTION:We define an explicit cohomology theory for topological groups
based on locally continuous measurable cochains. We study its functorial
properties and explore its relationship with other explicit cohomology the
ories.\nWe apply the theory to the case of connected Lie groups and certai
n modules and see that extension of a connected Lie group by coefficient m
odules of certain kind are connected Lie groups.\n\nhttps://indico.tifr.re
s.in/indico/conferenceDisplay.py?confId=403
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=403
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galois closure of essentially finite morphisms
DTSTART;VALUE=DATE-TIME:20100121T103000Z
DTEND;VALUE=DATE-TIME:20100121T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-419@cern.ch
DESCRIPTION:Let $X$ be a scheme over a field $k$ amd \n$f:Y\\to x$ an es
sentially finite morphism. We construct a `Galois closure' of $f$\, i.e\,
the smallest possible torsor dominating it. As an\napplication we constru
ct the Galois closure of towers of torsors. (Work in collaboration with Mi
chel Emsalem).\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py
?confId=419
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=419
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modularity of Galois representations
DTSTART;VALUE=DATE-TIME:20100128T103000Z
DTEND;VALUE=DATE-TIME:20100128T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-428@cern.ch
DESCRIPTION:The talk will describe my joint work with J-P.Wintenberger whi
ch proves Serre's cojecture. The initial breakthrough took place while I w
as at TIFR in the latter half of 2004\, while the complete proof was publi
shed at the end of 2009. In this talk I will focus on the consequences of
Serre's conjecture which verify the conjectures of Langlands and Fontaine-
Mazur for rank 2\, odd motives over the rationals. In particular\, we can
verify Artin's conjecture for 2-dimensional odd representations of the abs
olute Galois group of rationals. In the unlikely event that time permits I
will work out an exercise which uses this consequence to prove base chang
e for automorphic forms for odd A_5-type extensions of the rationals.\n\nh
ttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=428
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=428
END:VEVENT
BEGIN:VEVENT
SUMMARY:Combinatorial differential forms
DTSTART;VALUE=DATE-TIME:20100204T103000Z
DTEND;VALUE=DATE-TIME:20100204T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-472@cern.ch
DESCRIPTION:A degree n differential form on a manifold (or scheme) X is
generally thought of as a linear combination of n-th exterior products o
f 1-forms on X. I will discuss a more intuitive definition of such n-f
orms\, which sheds some light on a number of their properties. This will
be illustrated by considering the notion of a connection form on a princip
al G-bundle on X and its associated curvature 2-form. If time permits\, I
will then examine how these notions ca be extended to a categorified conte
xt. One is then led to consider a gerbe endowed with differential data con
sisting of a connection and a certain 2-form known as the B-field. Such da
ta then geometrically determines an associated curvature 3-form satisfying
a higher version of the Bianchi identity.\n\nhttps://indico.tifr.res.in/i
ndico/conferenceDisplay.py?confId=472
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=472
END:VEVENT
BEGIN:VEVENT
SUMMARY:Convex Projective Manifold of finite volume
DTSTART;VALUE=DATE-TIME:20100211T103000Z
DTEND;VALUE=DATE-TIME:20100211T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-485@cern.ch
DESCRIPTION:In my talk\, I will explain how covex projective geometry is a
generalisation of hyperbolic geometry. A convex projective manifold M is
the quotient of a properly open convex $\\omega$ set by a discrete group o
f projective transformation Gamma. The basic example of such manifold is
the quotient of the hyperbolic space by a discrete group of isometry. Thi
s kind of manifold carry a natural measure. A lot of people have studied t
he case where the manifold M is compact. I will explain what is known when
the dimension of M is 2 and how to construct such a manifold when\n$\\ome
ga$ is not the hyperbolic space. This will\nlead us\, to the construction
of discrete subgroup \nof $SL_n+1(\\mathbb (R)$.\n\nhttps://indico.tif
r.res.in/indico/conferenceDisplay.py?confId=485
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=485
END:VEVENT
BEGIN:VEVENT
SUMMARY:On certain curious aspects of finite-dimensionality phenomena aris
ing in functional analysis
DTSTART;VALUE=DATE-TIME:20100218T103000Z
DTEND;VALUE=DATE-TIME:20100218T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-502@cern.ch
DESCRIPTION:A property(P) of Banach spaces is said to be a finite-dimensio
nal property ((FD)-property\, for short) if it holds in all finite dimensi
onal Banach spaces but fails in each infinite dimensional Banach space. A
classical example of such a property is provided by the compactness of the
closed unit ball of a Banach space. At a less trivial level\, the equival
ence of absolute and unconditional convergence of series in a Banach space
provides yet another but perhaps one of the most imporatant examples of t
his phenomenon. We discuss some of the issues arising out of this\, in pa
rticular\, how it necessitates the introduction of Nuclear spaces (due to
Grothendieck) on the one hand and to the geometry of Banach spaces on the
other.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=50
2
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=502
END:VEVENT
BEGIN:VEVENT
SUMMARY:At the crossroad of algebra\, combinatorics and physics: a story o
f the mysterious and ubiquitous sequence 1\,2\,7\,42\,429\,...
DTSTART;VALUE=DATE-TIME:20100225T103000Z
DTEND;VALUE=DATE-TIME:20100225T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-522@cern.ch
DESCRIPTION:At the beginning of this century\, the physicists Razumov and
Stroganov discovered a certain sequence of integers appearing in the study
of some model for `quantum spin chains'. This sequence was already known
by combinatorists in the enumeration of various classes of combinatorial o
bjects: alternating sign matrices\, 3D partitions of integers\, tilling of
hexagons on a triangular lattice. In the last 30 years\, intensive studi
es have been made about these objects\, beautiful and simple conjectured e
numeration formulae had to wait for a long time before being proved. But m
any researches remain to be done in order to `understand' these formulae a
nd the relationship with quantum spin chains model in physics. No prerequi
sites are needed for this\ncolloquium\, neither in physics nor in combinat
orics. I will give a short introduction to enumerative combinatorics and w
ill finish by introducing a recent algebraic approach with operators and c
ommutations.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?con
fId=522
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=522
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zeta-functions and Weil-etale cohomology of number rings
DTSTART;VALUE=DATE-TIME:20100302T113000Z
DTEND;VALUE=DATE-TIME:20100302T123000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-535@cern.ch
DESCRIPTION:We will define Weil-etale Euler characteristics and explain ho
w they can be used to describe the behavior of the Dedekind zeta-function
at s = 0. We will also discuss how this might be extended to other integra
l values.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId
=535
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=535
END:VEVENT
BEGIN:VEVENT
SUMMARY:Are L-functions able to solve Diophantine equations ? - An introdu
ction to (non-commutative) Iwasawa theory.
DTSTART;VALUE=DATE-TIME:20100311T103000Z
DTEND;VALUE=DATE-TIME:20100311T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-550@cern.ch
DESCRIPTION:Starting from old problems in diophantine geometry\, we first
try to explain how Iwasawa was motivated to develop classical Iwasawa theo
ry. Then we describe the generalisations towards non-commutative Iwasawa t
heory and we shall make some comments on known results.\n\nhttps://indico.
tifr.res.in/indico/conferenceDisplay.py?confId=550
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=550
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Isomorphism Conjecture for groups acting on trees
DTSTART;VALUE=DATE-TIME:20100318T103000Z
DTEND;VALUE=DATE-TIME:20100318T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-557@cern.ch
DESCRIPTION:The Isomorphism conjecture of Farrell and Jones asserts that t
he K-theoretic (reduced projective class groups\, algebraic K-groups) and
the L-theoretic obstruction groups of a discrete group can be computed in
terms of the virtually cyclic subgroups of the group. A `virtually cyclic'
group\, by definition\, contains a cyclic subgroup of finite index. The
Isomorphism Conjecture implies several fundamental conjectures\, for examp
le the vanishing of the Whitehead group for torsion free discrete groups\,
Borel conjecture\, Novikov conjecture\, etc. We will study the conjecture
for groups acting on trees and see under what conditions on the vertex st
abilizers the conjecture can be deduced for the group.\n\nhttps://indico.
tifr.res.in/indico/conferenceDisplay.py?confId=557
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=557
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cyclic covers of $\\mathbb {A}^2$
DTSTART;VALUE=DATE-TIME:20100415T103000Z
DTEND;VALUE=DATE-TIME:20100415T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-601@cern.ch
DESCRIPTION:A $\\mathbb {Q}$-homology plane is by definition\na smooth aff
ine algebraic surface $X$ such that\n$h_i(X\;\\mathbb {Q})=(0)$ for $i>0.
We shall\ntalk about the classification of smooth affine\nalgebraic surfac
es $z^n=f(x\,y)$ which are\n$\\mathbb {Q}$-homology plane.\n\nhttps://indi
co.tifr.res.in/indico/conferenceDisplay.py?confId=601
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=601
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maximal linear sections of Grassmannians
DTSTART;VALUE=DATE-TIME:20100422T103000Z
DTEND;VALUE=DATE-TIME:20100422T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-610@cern.ch
DESCRIPTION:Consider a finite dimensional vector space over a field and th
e collection of all its subspaces of a fixed dimension. It is well-known t
hat this constitutes a nice geometric object\, namely\, the Grassmannian w
ith its canonical Plucker embedding. Linear sections of Grassmanians\, of
which Schubert varieties in Grassmannians are special cases\, are interest
ing objects from algebraic\, topological and combinatorial viewpoints. We
consider the following question: Among the sections of Grassmannians by li
near subspaces of a fixed dimension of the Plucker projective space\, whic
h are ``maximal'' ? The\nterm `maximal' can be interpreted in several ways
and we will be particularly interested in maximality with respect to the
number of points\, when working over a finite field. In general\, this\ni
s an open problem. ..........(contd) An attempt will be made to keep the p
rerequisites at a minimum.\n\nhttps://indico.tifr.res.in/indico/conference
Display.py?confId=610
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=610
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fibre Bundles
DTSTART;VALUE=DATE-TIME:20100617T103000Z
DTEND;VALUE=DATE-TIME:20100617T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-675@cern.ch
DESCRIPTION:Topology studies objects which are locally simple but globally
complicated. An important class of such objects are fiber bundles\, which
are globally `twisted'. The simplest example is a Mobius band. The amount
of global twist is quantified by algebraic invariants. This talk will giv
e an elementary introduction to the subject of Fiber Bundles and their inv
ariants. (This\ntalk is intended for the VSRP students of\nSchool of Mathe
matics).\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
675
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=675
END:VEVENT
BEGIN:VEVENT
SUMMARY:Class field theory
DTSTART;VALUE=DATE-TIME:20100624T103000Z
DTEND;VALUE=DATE-TIME:20100624T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-682@cern.ch
DESCRIPTION:CFT classifies abelian extensions of number fields. We discuss
some basic results in the \narea\, focussing on the very beautiful proper
ties of the Hilbert class field.\n[This colloquium is meant for the VSRP s
tudents ]\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId
=682
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=682
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weyl's equidistribution criterion
DTSTART;VALUE=DATE-TIME:20100701T103000Z
DTEND;VALUE=DATE-TIME:20100701T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-692@cern.ch
DESCRIPTION:A sequence $\\{x_1\, x_2\, \\ldots \\}$ of real numbers in [0\
,1] is said to be equidistributed if \\lim_{n\\mapsto \\infty} |\\{x_1\, \
\ldots\, x_n\\} \\cap [a\,b]|/n = b-a$ for all $[a\,b] \\subset [0\,1]$.
In this talk\, we will prove a result due to Hermann Weyl on equidistribut
ed sequences\, and discuss some applications. [This colloquium talk is m
eant for the VSRP students of School of Mathematics]\n\nhttps://indico.tif
r.res.in/indico/conferenceDisplay.py?confId=692
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=692
END:VEVENT
BEGIN:VEVENT
SUMMARY:Permanents\, matchings and van der Waerdens conjecture.
DTSTART;VALUE=DATE-TIME:20100708T103000Z
DTEND;VALUE=DATE-TIME:20100708T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-695@cern.ch
DESCRIPTION:In 1926 van der Waerden conjectured that the minimum value of
the permanent of a doubly stochastic matrix is $\\frac {n!}{n^n}$. This w
as proved by Egorychev and Falikman in 1980. Their proofs used special ca
se of Alexandorff-Fenchel inequalities. In this talk we will see an outlin
e of a very simple proof using hyperbolic polynomials (due to Leonid Gurvi
ts\, 2008) and its applications in various graph matching counting problem
s. \n[This colloquium is meant for the VSRP students].\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=695
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=695
END:VEVENT
BEGIN:VEVENT
SUMMARY:Endomorphism Algebras of modular motives
DTSTART;VALUE=DATE-TIME:20100715T103000Z
DTEND;VALUE=DATE-TIME:20100715T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-709@cern.ch
DESCRIPTION:Let $f = \\sum_{n = 1}^\\infty a_n q^n$ be a primitive non-CM
(non dihedral for weight one) cusp form of weight $k \\geq 1$\, level $N \
\geq 1$ and and character $\\epsilon$\, and $M_f$ be the motive attached
to $f$. \n................contd................. In this talk\nwe will giv
e a complete description of the Brauer class of $X_f$ in terms of the slop
es of the adjoint lift of $f$\, under a finiteness hypothesis on these slo
pes. We also extend the above results to the simpler case of non-dihedral
modular forms of weight one\, where the Grothendieck motive is replaced by
an Artin motive.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.p
y?confId=709
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=709
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rational points on sub-varieties of semi-abelian varieties\, an ov
erview
DTSTART;VALUE=DATE-TIME:20100719T103000Z
DTEND;VALUE=DATE-TIME:20100719T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-712@cern.ch
DESCRIPTION:Starting from the solution of the Mordell-Lang conjecture abou
t two decades ago\, we shall go through the various progresses that have b
een made since\, especially during the last decade: counting the solutions
and uniformity questions\; varying the underlying group. The link with th
e study of points of small height and recent results in that line will als
o be discussed.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?
confId=712
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=712
END:VEVENT
BEGIN:VEVENT
SUMMARY:Grothendieck-Witt groups and projective modules
DTSTART;VALUE=DATE-TIME:20100903T090000Z
DTEND;VALUE=DATE-TIME:20100903T100000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-780@cern.ch
DESCRIPTION:We will present new developments in the theory of Grothendiec
k-Witt groups (aka Hermitian K-theory)\, and then give some nice applicati
ons. In particular\, we will prove Suslin's conjecture that stably free mo
dules of rank d - 1 over a smooth affine algebra of dimension d over an
algebraically closed field are free.\n\nhttps://indico.tifr.res.in/indico
/conferenceDisplay.py?confId=780
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=780
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Cauchy-Riemann Equations on a Product Domain
DTSTART;VALUE=DATE-TIME:20100909T103000Z
DTEND;VALUE=DATE-TIME:20100909T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-789@cern.ch
DESCRIPTION:Solving the Cauchy-Riemann\, or ($\\overline{\\partial}$ equat
ions with estimates is a central question in multidimensional complex anal
ysis. For strongly pseudoconvex domains\, or more generally for domains of
finite type\, such estimates are classical and go back to the work of Koh
n. This approach fails for many interesting domains\, for example\, produc
t domains. We discuss some new results (joint with Mei-Chi Shaw) regarding
regularity of the solutions of the $\\overline{\\partial}$-equation on pr
oduct domains.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?c
onfId=789
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=789
END:VEVENT
BEGIN:VEVENT
SUMMARY:Generalised modular functions and their characters
DTSTART;VALUE=DATE-TIME:20100917T090000Z
DTEND;VALUE=DATE-TIME:20100917T100000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-803@cern.ch
DESCRIPTION:Generalized modular functions are holomorphic functions on the
complex upper half-plane that satisfy the usual transformation formula of
a classical modular functions\, with the sole exception that the characte
r need not be unitary. The theory partly is motivated from CFT in Physics.
We will report on very recent joint work (2010) with G. Mason on the char
acters and Fourier coefficients of such functions.\n\nhttps://indico.tifr.
res.in/indico/conferenceDisplay.py?confId=803
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=803
END:VEVENT
BEGIN:VEVENT
SUMMARY:What is the Fundamental Lemma ?
DTSTART;VALUE=DATE-TIME:20100923T103000Z
DTEND;VALUE=DATE-TIME:20100923T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-811@cern.ch
DESCRIPTION:Unlike most recent talks about the Fundamental Lemma recently
proved by Ngo\, who was awarded with a Fields Medal for this achievement\,
I'll not say anything at all about what Ngo did. Instead\, I talk about t
he origins of the Fundamental Lemma in work of Langlands\, trying to give
some idea of a few simple cases.\n\nhttps://indico.tifr.res.in/indico/conf
erenceDisplay.py?confId=811
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=811
END:VEVENT
BEGIN:VEVENT
SUMMARY:Positivity of relative canonical bundles and applications
DTSTART;VALUE=DATE-TIME:20100930T103000Z
DTEND;VALUE=DATE-TIME:20100930T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-828@cern.ch
DESCRIPTION:Given an effectively parameterized family of canonically polar
ized manifolds the Kahler-Einstein metrices on the fibres induce a hermiti
an metric on the relative canonical bundle. We use a global elliptic equa
tion to show that this metric is strictly positive and give estimates. For
degenerating families it turns out that the curvature form on the total s
pace can be controlled. By fiber integration it is shown that the generali
zed Weil-Petersson form on the base possesses an extension as a positive c
urrent. In this situation\, the determinant line bundles associated to the
relative canonical bundle on the total space can be extended. As an appl
ication we obtain a short analytic proof of the quasiprojectivity of the m
oduli space ${\\mathcal M}_{\\mathrm {can}}$ of canonically polarized vari
eties. Further applications about curvature on higher direct image sheaves
and hyperbolicity of moduli spaces are mentioned.\n\nhttps://indico.tifr.
res.in/indico/conferenceDisplay.py?confId=828
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=828
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weil conjectures for the moduli stack of vector bundles on algebra
ic curves.
DTSTART;VALUE=DATE-TIME:20101007T103000Z
DTEND;VALUE=DATE-TIME:20101007T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-846@cern.ch
DESCRIPTION:After a brief introduction to moduli problems and moduli stack
s\, I will explain how to calculate the l-adic cohomology ring of the modu
li stack of vector bundles on an algebraic curve in positive characteristi
c\, discuss actions of the various Frobenius morphisms and how to prove an
analogue of the classical Weil conjectures for the moduli stack.\n\nhttps
://indico.tifr.res.in/indico/conferenceDisplay.py?confId=846
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=846
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the nonabelian Tensor Product and the Box-Tensor product of gro
ups
DTSTART;VALUE=DATE-TIME:20101014T103000Z
DTEND;VALUE=DATE-TIME:20101014T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-857@cern.ch
DESCRIPTION:The nonabelian tensor product of groups arose in connection wi
th homotopy theory. It was introduced by R. Brown and J.-L. Loday\, extend
ing ideas of J.H.C. Whitehead. A special case\, the nonabelian tensor squa
re\, already appeared in the work of R.K. Dennis where it arises in connec
tion with K-theory. We introduce the nonabelian tensor product and the box
-tensor product of two groups and discuss various properties of these grou
ps.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=857
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=857
END:VEVENT
BEGIN:VEVENT
SUMMARY:Polynomial representations of GL(n\,C) and related combinatorics.
DTSTART;VALUE=DATE-TIME:20101021T103000Z
DTEND;VALUE=DATE-TIME:20101021T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-871@cern.ch
DESCRIPTION:I will give an elementary introduction to polynomial represent
ations of the complex general linear group and related combinatorics.\n\nh
ttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=871
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=871
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non vanishing of Jacobi Poincar\\'e series and the structure of He
rmitian Jacobi forms.
DTSTART;VALUE=DATE-TIME:20101028T103000Z
DTEND;VALUE=DATE-TIME:20101028T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-908@cern.ch
DESCRIPTION:It is known that the Poincar\\'e series span the space of cusp
forms for several types of modular forms. However it is in general an ope
n question to decide which of them do not vanish identically. We give some
sufficient conditions for the non vanishing of Poincar\\'e series for Jac
obi group over the integers. We also discuss several structural properties
of Hermitian Jacobi forms and some questions related to their structure a
s a module over the algebra of elliptic modular forms.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=908
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=908
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hecke Modifications\, Wonderful Compactifications and Moduli of Pr
incipal Bundles
DTSTART;VALUE=DATE-TIME:20101104T103000Z
DTEND;VALUE=DATE-TIME:20101104T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-919@cern.ch
DESCRIPTION:A Hecke modification of holomorphic principal bundle over a Ri
emann surface is obtained by twisting the transition function in a neighbo
urhood of a point. The spaces of such modifications can be described in te
rms of the Bruhat cells of the associated affine Grassmanian. Thus\, one c
an form families of principal bundles parametrized by such spaces. When th
e group is semisimple of adjoint type\, one can use the wonderful (De Conc
ini-Procesi) compactification to obtain parametrizations of the moduli spa
ce of bundles in certain cases. The aim of this talk will be to describe t
he constructions just mentioned and to outline how the parametrization is
obtained.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId
=919
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=919
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eisenstein series in the cohomology of locally symmetric spaces
DTSTART;VALUE=DATE-TIME:20101111T103000Z
DTEND;VALUE=DATE-TIME:20101111T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-932@cern.ch
DESCRIPTION:Locally symmetric spaces and their cohomology (Betti\, de Rham
\, Lie algebra etc.) are ubiquitous in number theory and geometry for vari
ous reasons\, one being the fact that they lie at the heart of the theory
of automorphic forms. Taking this point of view\, I will explain and illus
trate in terms of examples how Eisenstein series can be used to identity a
nd construct non-trivial classes in the context of these cohomology theori
es.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=932
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=932
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cycles on a generic complex abelian 3-fold
DTSTART;VALUE=DATE-TIME:20101118T103000Z
DTEND;VALUE=DATE-TIME:20101118T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-954@cern.ch
DESCRIPTION:The Chow groups CH^i(X) of a complex projective manifold X hav
e a rather complicated structure\, in general\, but one might hope that a
for a prime p\, the p-torsion and p-cotorsion subgroups are more easy to u
nderstand. \nI will first survey the `classical' finiteness results for th
e p-torsion and p-cotorsion\, and then discuss examples\, based on joint w
ork with A.Rosenschon\, to show that outside this classical realm\, the p-
torsion and p-cotorsion are in general infinite. Our work builds on earlie
r works of Ceress\, Nori\, Bloch-Esnault and Schoen\, which I will also di
scuss briefly.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?c
onfId=954
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=954
END:VEVENT
BEGIN:VEVENT
SUMMARY:Two questions on holomorphic mappings between domains in C^n
DTSTART;VALUE=DATE-TIME:20101121T210000Z
DTEND;VALUE=DATE-TIME:20101121T220000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-979@cern.ch
DESCRIPTION:Abstract yet to receive.\n\nhttps://indico.tifr.res.in/indico/
conferenceDisplay.py?confId=979
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=979
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Local Galois Representations attached to Automorphic Forms
DTSTART;VALUE=DATE-TIME:20101202T103000Z
DTEND;VALUE=DATE-TIME:20101202T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-997@cern.ch
DESCRIPTION:In arithmetic\, Galois representations are one of the fundamen
tal objects of interest and they arise quite naturally in several places.
The Galois representations coming from cuspidal automorphic forms on $\\ma
thrm{GL}_n(\\mathbb {A}_{\\mathbb {Q}$ are expected to be irreducible as r
epresentatins of the absolute Galois group of $\\mathbb{Q}$. However\, the
local representations\, obtained by restricting to a decomposition subgro
up\, can be reducible. In this talk\, we will show how a generalized notio
n of ordinariness for automorphic forms implies the reducibility of such l
ocal representations. We also show that non-ordinariness implies irreducib
ility in certain cases. When $n=2$ and $p=2$\, we will also discuss the se
misimplicity of local Galois representations attached to ordinary cuspidal
eigenforms\, following the approach of Ghate-Vatsal for odd primes. This
requires proving some new results in Hida theory for the prime $p=2$.\n\nh
ttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=997
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=997
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometry and dynamics of Kleinian groups
DTSTART;VALUE=DATE-TIME:20101214T090000Z
DTEND;VALUE=DATE-TIME:20101214T100000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1019@cern.ch
DESCRIPTION:Kleinian groups are discrete subgroups of the Isometry group o
f hyperbolic 3-space. Their\nlimit sets are the points of accumulation of
orbits on the ideal boundary. The most representative examples are surface
Kleinian groups\, i.e\, discrete faithful representations of \\pi_1(S) in
to \nPSL_2(C). We shall describe a rigidity result (due to Minsky et al)
and a result\ndue to the author that says that limit sets are \\pi_1(S)-eq
uivariant quotients of the\ncircle.\n\nhttps://indico.tifr.res.in/indico/c
onferenceDisplay.py?confId=1019
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1019
END:VEVENT
BEGIN:VEVENT
SUMMARY:Visibility and the Birch and Swinnerton-Dyer conjecture for analyt
ic rank one
DTSTART;VALUE=DATE-TIME:20101216T103000Z
DTEND;VALUE=DATE-TIME:20101216T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1028@cern.ch
DESCRIPTION:Let E be an (optimal) elliptic curve over the rational numbers
such that the L-function of E vanishes to order one at s=1. Then by work
of Gross and Zagier\, there is a point on E defined over a suitable quadra
tic imaginary field K\, called a Heegner point\, that has infinite order.
Furthermore\, they showed that the second part of the Birch and Swinnerton
-Dyer conjecture then predicts that the index of the cyclic group generate
d by the Heegner point in the group of K-rational points on E is the produ
ct of the order of the Shafarevich-Tate group of E over K and certain oth
er integer invariants of E. In our talk\, we will extract a factor from th
e index mentioned above\, and use the theory of visibility to show that if
an odd prime divides this factor\, then it divides the order of the Shafa
revich-Tate group (as predicted)\, under certain hypotheses\, the most ser
ious of which is the first part of the Birch and Swinnerton-Dyer conjectur
e.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1028
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1028
END:VEVENT
BEGIN:VEVENT
SUMMARY:On polynomial maps from C^2 to C and to C^2
DTSTART;VALUE=DATE-TIME:20101223T103000Z
DTEND;VALUE=DATE-TIME:20101223T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1038@cern.ch
DESCRIPTION:The topic of the talk is the study of the fibers of polynomial
maps from C^2 to C and to C^2. We will see the existence of generic fiber
s. We will introduce the tools to detect\nwhich fibers are generic and to
study all the fibers. We will end with some open problems.\n\nhttps://indi
co.tifr.res.in/indico/conferenceDisplay.py?confId=1038
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1038
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cohomology jumping loci of arrangement complements and beyond
DTSTART;VALUE=DATE-TIME:20101224T103000Z
DTEND;VALUE=DATE-TIME:20101224T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1039@cern.ch
DESCRIPTION:We will discuss two examples of the sets (`loci') in the title
: resonance varieties and characteristic varieties of topological spaces w
ith more emphasis on the former. Theory of these varieties per se and thei
r many applications have been developed mostly for hyperplane arrangement
complements. Recently some of their properties have been generalized to wi
der classes of spaces like complex quasiprojective varieties\, formal spac
es and toric complexes. We will survey as many of these topics as time all
ows.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1039
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1039
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rational Points and Motivic Integration
DTSTART;VALUE=DATE-TIME:20110106T103000Z
DTEND;VALUE=DATE-TIME:20110106T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1065@cern.ch
DESCRIPTION:We give a positive ansawer to a question by \nSerre over char.
0 strictly henselian fields asserting the existence of fixed rational poi
nts of a finite $\\ell$- group action on the affine space\, using motivic
integration. Here $\\ell$ is different from the residue characteristic.
(Joint with Johannes Nicaise)\n\nhttps://indico.tifr.res.in/indico/confer
enceDisplay.py?confId=1065
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1065
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modular degrees of elliptic curves
DTSTART;VALUE=DATE-TIME:20110113T103000Z
DTEND;VALUE=DATE-TIME:20110113T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1081@cern.ch
DESCRIPTION:Modular degree is an interesting invariant of elliptic curves.
It is computed by a variety of methods. After computer calculations\, Wat
kins conjectured that given $E/\\mathbb {Q} of rank $R\, 2^R$ devides $\\d
eg (\\Phi)$\, where $\\Phi : X_0(N) \\to E$ is the optimal map (up to isom
orphism of E) and $\\deg (\\Phi)$ is the modular degree of E. In fact\, he
observed that $2^{R+K}$ should divide the modular degree with $2^K$ depen
ding on W\, where W is the group of Atkin-Lehner involutions\, \n\\mid W \
\mid = 2^{\\omega(N)}\, N$ is the conductor of the elliptic curve and $\\o
mega (N)$ counts the number of distinct prime factors of N. We have prove
d that $2^{R+K}$ divides $\\deg (\\Phi)$ would follow from an isomprphism
of complete intersection rings of a universal deformation ring and a Hecke
ring\, where $2^K = \\mid W^{\\prime} \\mid $\, the cardinality of a cert
ain subgroup of the group of Atkin-Lehner involutions.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=1081
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1081
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tamagawa numbers of algebraic groups and geometry
DTSTART;VALUE=DATE-TIME:20110120T103000Z
DTEND;VALUE=DATE-TIME:20110120T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1095@cern.ch
DESCRIPTION:We will begin by recalling the definition of the Tamagawa numb
er of an algebraic group. In the late 1970's\, Harder posed a conjecture r
elating this invariant to moduli spaces of G-bundles. The general form of
this conjecture remains open. Harder's conjecture was reinterpreted using
the trace formula for stacks by Behrend. This approach settled the conject
ure in certain special cases. We will end with a discussion of recent work
of Heinloth and Schmitt.\n\nhttps://indico.tifr.res.in/indico/conferenceD
isplay.py?confId=1095
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1095
END:VEVENT
BEGIN:VEVENT
SUMMARY:New results on Subgroups of Classical Groups
DTSTART;VALUE=DATE-TIME:20110127T103000Z
DTEND;VALUE=DATE-TIME:20110127T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1109@cern.ch
DESCRIPTION:We give an account of some recent results on description of su
bgroups of a [classical] Chevalley group $G{\\Phi\, R)$ of type $\\Phi$\no
ver a commutative ring $R$\, containing an elementary subgroup of $\\Phi(E
(\\Delta\, A))$ in a rational representation $\\Phi$. A natural context to
specify broad classes of large semi-simple subgroups in classical groups
is provided by Aschbacher's subgroup structure theorem and its generalisa
tion to exceptional groups by Liebeck and Seitz. Until recently\, little w
as known on description of subgroups from Aschbacher classes. The only cas
e which was completely settled in the 1980-ies\, originally by Borewics an
d the author\, were overgroups of subsystem subgroups\, class C_1+C_2. Ge
neralisations of these results to other classes were widely discussed\, bu
t no definitive results were in sight until 2000. Over the last decade the
situation changed dramatically. ...........contd.....\n................
..Here\, one should from the very start take account of the effects from t
he theory of algebraic groups\, whereas the proofs heavily rely on the pow
er of localisation methods\, such as Quillen - Suslin - Vaserstein localis
ation and patching\, or Bak's localisation-completion.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=1109
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1109
END:VEVENT
BEGIN:VEVENT
SUMMARY:What can an algebraic geometer do for Euclidean geometry ?
DTSTART;VALUE=DATE-TIME:20110203T103000Z
DTEND;VALUE=DATE-TIME:20110203T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1125@cern.ch
DESCRIPTION:I will begin with the 3rd problem of Hilbert on the scissors c
ongruence groups of Euclidean spaces. Then as we go a bit further\, I will
explain how this is related to some number theory problems\, and some dee
p algebro-geometric problems in motives\, as well as some remote fields su
ch as cyclic homology.\n\nhttps://indico.tifr.res.in/indico/conferenceDisp
lay.py?confId=1125
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1125
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stability and Hermitian-Einstein metrics for vector bundles on fra
med manifolds
DTSTART;VALUE=DATE-TIME:20110210T103000Z
DTEND;VALUE=DATE-TIME:20110210T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1147@cern.ch
DESCRIPTION:We adapt the notions of stability in the sense of Mumford-Take
moto and Hermitian-Einstein metrics for holomorphic vector bundles on cano
nically polarized framed manifolds\, i.e. compact complex manifolds X toge
ther with a smooth divisor D such that the canonical divisor of X plus D
is ample. It turns out that the degree of a torsion-free coherent sheaf on
X with respect to this polarization coincides with the degree with respec
t to the complete Kaehler-Einstein metric g on the complement of D in X. F
or stable holomorphic vector bundles\, we prove the existence of a Hermiti
an-Einstein metric with respect to g and also the uniqueness in an adapted
sense.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1
147
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1147
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weyl Character and super-character formulae for finite dimensional
and affine Lie superalgebras with symmetrizable Cartan matrices
DTSTART;VALUE=DATE-TIME:20110303T103000Z
DTEND;VALUE=DATE-TIME:20110303T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1211@cern.ch
DESCRIPTION:For finite dimensional simple and ffine Lie algebras\, the roo
ts of positive norm are all real\, i.e. act locally finitely on integrable
modules\, whereas the roots of non-positive norm do not\, and the nondiag
onal entries of the Cartan matrices are non-positive. For most finite dime
nsional and affine Lie superalgebras there are roots both positive and neg
ative non-diagonal entries in the Cartan matrices. Hence the usual proofs
aof the character formula do not work and computing these characters in al
l cases has remained an open problem for the last twenty years. The greate
r the dimension of the maximal isotropic\, subspace of the set of roots\,
the greater the complication. In this talk\, I will explain my recent proo
f of these formulae.\n\nhttps://indico.tifr.res.in/indico/conferenceDispla
y.py?confId=1211
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1211
END:VEVENT
BEGIN:VEVENT
SUMMARY:Approximation of algebraic numbers by algebraic numbers of given d
egree
DTSTART;VALUE=DATE-TIME:20110307T103000Z
DTEND;VALUE=DATE-TIME:20110307T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1219@cern.ch
DESCRIPTION:It is well known that irrational algebraic numbers are badly a
pproximated by rational numbers and this is best quantified in the celebra
ted Roth theorem. This theorem was extended to simultaneous approximation
of several algebraic numbers as a consequence of Schmidt subspace theorem.
Schmidt also extended Roth theorem to the approximation of an algebraic
number by algebraic numbers of given smaller degree (over the field of ra
tional numbers). We will present a result that combines both extensions\,
obtained in collaboration with Hans Peter Schlickewei. An interesting feat
ure is that our estimate shows a distinct behaviour in comparison with the
subspace theorem\, however it is not optimal with respect to the number o
f algebraic numbers considered.\n\nhttps://indico.tifr.res.in/indico/confe
renceDisplay.py?confId=1219
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1219
END:VEVENT
BEGIN:VEVENT
SUMMARY:Characterization of eigenfunctions of the Laplacian on Riemannian
symmetric spaces of noncompact type
DTSTART;VALUE=DATE-TIME:20110310T103000Z
DTEND;VALUE=DATE-TIME:20110310T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1220@cern.ch
DESCRIPTION:A result of real analysis (John Roe 1980) states that if all d
erivatives and antiderivatives of a measurable function f are uniformly bo
unded then f is a linear combination of $\\sin x$ and $\\cos x$. This res
ult was extended to $\\mathbb{R}^n$ independently by Howard and Reese (199
2) and by Strichartz (1993) where the derivatives and antiderivatives are
substituted by integral powers of Laplacian on $\\mathbb{R}^n$. While iti
s plausible to extend this theorem for other Riemannian manifolds\, Strich
artz showed that the result holds true for Heisenberg groups\, but fails f
or hyperbolic spaces. Hyperbolic spaces are the most distinguished protot
ypes of the rank one Riemannian symmetric spaces of noncompact type. Stric
hartz's counter example can be extended to this larger class. In this talk
we shall try to find the root cause of this failure and explore the possi
bility of extending this theorem for this class of spaces.\n\nhttps://indi
co.tifr.res.in/indico/conferenceDisplay.py?confId=1220
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1220
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Jacobian conjecture
DTSTART;VALUE=DATE-TIME:20110317T103000Z
DTEND;VALUE=DATE-TIME:20110317T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1230@cern.ch
DESCRIPTION:Let $\\phi = (f\,g): C^2 \\rightarrow C^2$ be a polynomial map
of the plane over the field C of complex numbers with its Jacobian nonzer
o constant. The Jacobian conjecture asserts that $\\phi$ must be an automo
rphism. We say that a point $P_infty \\in P^2 \\C^2$ of the complex projec
tive plane P^2 is a `quasifinite' (w.r.t. \\phi)$ if there exists a sequen
ce \n$\\{P_i\\}$ in $C^2 \\in P^2$ converging\nto $P_\\infty$ such that th
e image $\\{\\phi(P_i)\\}$ converges to a point in\nC^2. In this talk I wi
ll show that the conjecture holds if any only if there is no quasifinite p
oint.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=123
0
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1230
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some results on finite generation of algebras of certain type
DTSTART;VALUE=DATE-TIME:20110324T103000Z
DTEND;VALUE=DATE-TIME:20110324T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1253@cern.ch
DESCRIPTION:Let R be a commutative Noetherian domain and A an integral dom
ain containing R. For a prime ideal P in R\, we denote by $k(P)$ the resi
due field $R_p/PR_p$ of the local ring $R_p$. Then the ring $k(P) \\otime
s_R A$ is called the fibre of A over R at P. Let $\\Delta$ be a subset of
${\\rm Spec }(R)$\, and suppose that the structure of fibre $k(P)\\otimes_
R A$ is given for every P in \n$\\Delta$. Then what can we say about the s
tructure of A as an R-algebra? This is an interesting and important proble
m of commutative algebra. In this talk I shall present some results regard
ing this problem focussed on finite generation of A over R.\n\nhttps://ind
ico.tifr.res.in/indico/conferenceDisplay.py?confId=1253
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1253
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Intersection of Annihilator of the Valabrega-Valla Module
DTSTART;VALUE=DATE-TIME:20110331T103000Z
DTEND;VALUE=DATE-TIME:20110331T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1265@cern.ch
DESCRIPTION:Let $(A\, \\mathfrak{m})$ be a Cohen-Macaulay local ring with
an infinite residue field and let $I$ be an $\\mathfrak{m}$-primary ideal.
If $J=(x_1\, \\ldots\, x_s)$ is a minimal reduction of $I$ then consider
the $A$-module\n$$\\mathcal{V}_I(J) = \\bigoplus_{n\\geq 1} \\frac{I^{n+1}
\\cap J} {JI^n}.$$ \nA consequence of a theorem due to Valabrega and Val
la is that $\\mathcal{V}_I(J) = 0$ if and only if $G_I(A)$ is Cohen-Maca
ulay. We show that if $G_I(A)$ is not Cohen-Macaulay then \n$$\\bigcap {\\
substack {\\text{$J$ minimal} \\\\ \\text{reduction of $I$}}} \\operatorna
me{\\ann}_A {\\mathcal V}_I{J} \\qad \\text{is} \\mathfrak{m} \\text{-prim
ary}.$$\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1
265
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1265
END:VEVENT
BEGIN:VEVENT
SUMMARY:Two classical results in Additive Combinatorics: Some related rece
nt results
DTSTART;VALUE=DATE-TIME:20110407T103000Z
DTEND;VALUE=DATE-TIME:20110407T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1287@cern.ch
DESCRIPTION:Let G be an abelian group\, and A and B be finite subsets of G
. The sumset A+B is the set of all elements of G that can be written in th
e form a+b\, where $a \\in A$ and \n$b \\in B$. Given a subset A of G\, de
termining properties of the h-fold sumset hA is a direct problem for addit
ion in groups. In particular\, Langrange's theorem that every nonnegative
integer is a sum of four squares is an example of a direct problem. Also\,
for a finite set A\, denoting its cardinality by |A|\, finding a lower bo
und for |A+B| in terms of |A|and |B| is a direct problem. An inverse probl
em\, on the other hand\, is one where a knowledge of the size of hA gives
some information about A. In this lecture\, first we have some introducto
ry discussion about the nature of these problems. Then we take up a classi
cal result in direct problems where G is the cyclic group of prime order a
nd sketch a recent proof of it among other things. Next\, as an applicatio
n of this\, we more on to discuss the EGZ Theorem\, a prototype of zerosu
m theorems. We shall also discuss on some related constants and some new d
evelopments.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?con
fId=1287
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1287
END:VEVENT
BEGIN:VEVENT
SUMMARY:Around the local index formula
DTSTART;VALUE=DATE-TIME:20110421T103000Z
DTEND;VALUE=DATE-TIME:20110421T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1320@cern.ch
DESCRIPTION:Connes-Moscovici Local Index Formula expresses the index pairi
ng in terms of sums of certain residues. However this formula can be appli
ed if certain hypothesis holds. I want to talk about a weakening of the he
at kernel expansion and a transformation which implies stability of the hy
pothesis. I will definitely talk about the basic ingredients of the subjec
t and a quick application by Connes\, of some of the ideas towards the no
idempotent conjecture for the group ring of free group on two generators.
After that if time permits\, I'll talk about the local index formula.\n\nh
ttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1320
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1320
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algebraic Curves
DTSTART;VALUE=DATE-TIME:20110616T103000Z
DTEND;VALUE=DATE-TIME:20110616T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1432@cern.ch
DESCRIPTION:We will look at algebraic curves defined by a polynomial equat
ion inside a 2 dimensional complex space. Using the tools of algebra\, top
ology\, calculus of several variables and complex analysis\, we will show
that if the polynomial is irreducible then such a curve is connected.(This
is is a colloquium meant for the VSRP \nMaths. Students.\n\nhttps://indic
o.tifr.res.in/indico/conferenceDisplay.py?confId=1432
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1432
END:VEVENT
BEGIN:VEVENT
SUMMARY:Finding integral points in regions of euclidean spaces
DTSTART;VALUE=DATE-TIME:20110623T103000Z
DTEND;VALUE=DATE-TIME:20110623T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1441@cern.ch
DESCRIPTION:Given a region in a euclidean space under what conditions\, sa
y on its shape\, size etc\, can we conclude that it must contain a point w
ith integer coordinates ? This problem is relevant in various contexts and
has been attacked through various techniques. We shall discuss some of th
e techniques and results on the problem.\n(This talk is primarilly meant f
or the VSRP students of the School of Maths.)\n\nhttps://indico.tifr.res.i
n/indico/conferenceDisplay.py?confId=1441
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1441
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geometry's intervention in arithmetic
DTSTART;VALUE=DATE-TIME:20110630T103000Z
DTEND;VALUE=DATE-TIME:20110630T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1457@cern.ch
DESCRIPTION:The developments in geometry and arithmetic i.e. Number Theory
ran parallel for \nmany centuries until Descartes appeared on the scene a
nd showed how algebra can be\npressed into the service of geometry. But th
ings work the other way too: Geometry\nhas had a decisive role in proving
theorems in number theory. In this talk\, I will\nillustrate this by a sim
ple example: the determination of all Pythagorean triplets\nof integers. \
n\n[This talk is primarilly meant for the VSRP Maths. students]\n\nhttps:/
/indico.tifr.res.in/indico/conferenceDisplay.py?confId=1457
LOCATION:Colaba Campus AG66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1457
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representations of numbers as sums of squares
DTSTART;VALUE=DATE-TIME:20110707T103000Z
DTEND;VALUE=DATE-TIME:20110707T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1492@cern.ch
DESCRIPTION:A famous theorem of Lagrange states that every nonnegative in
teger n can be \nexpressed as a sum of 4 squares. A natural question th
en arises: in how\nmany ways can you do it\, as a function of n ? I will
discuss this question\, \nand similar ones\, by making connections with mo
dular forms.\n\n[This talk is primarilly meant for the VSRP students of ma
thematics.]\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?conf
Id=1492
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1492
END:VEVENT
BEGIN:VEVENT
SUMMARY:On spectral analogues of strong multiplicity one theorem
DTSTART;VALUE=DATE-TIME:20110714T103000Z
DTEND;VALUE=DATE-TIME:20110714T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1506@cern.ch
DESCRIPTION:We prove various spectral analogues of the classical strong mu
ltiplicity one\ntheorem in the context of compact locally symmetric Rieman
nian manifolds. We\nalso prove an analogue of the strong multiplicity one
theorem for the length spectrum for even dimensional compact hyperbolic sp
aces. This is a joint work\nwith Prof. C.S. Rajan.\n\nhttps://indico.tifr.
res.in/indico/conferenceDisplay.py?confId=1506
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1506
END:VEVENT
BEGIN:VEVENT
SUMMARY:Optimal points for a probability distribution on a Cantor set
DTSTART;VALUE=DATE-TIME:20110721T103000Z
DTEND;VALUE=DATE-TIME:20110721T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1512@cern.ch
DESCRIPTION:Given a probability measure $P$ on a compact subset\nof ${\\m
athbb R}^d$ and a natural number $n$\, the {\\it{$n$th quantization error
of\n$P$} is defined to be\n\n$$V_n=\\inf_{\\ga} \\int \\min_{a\\in\\ga} \\
|x-a\\|^2 dP(x)\,$$\n\nwhere the infimum is taken over all subsets $\\alph
a$ of ${\\mathbb R}^d$ with\ncard $\\alpha\\leq n$\, and $\\| \\cdot\\|$ d
enotes the Euclidean norm on ${\\mathbb\nR}^d$. A set $\\alpha$ for which
the infimum is\nachieved is called a {\\it {$n$-optimal set}. \nThe {\\it
{Quantization dimension} for the probability measure $P$\nis defined by\n\
n$$D(P)=\\lim_{n\\to \\infty} \\frac{2\\log n}{-\\log V_n}\,$$\n\nand corr
esponds to the rate how fast $V_n$ goes to zero as $n$ tends\nto infinity.
\n\nIn this talk\, we consider the Cantor set equipped with the natural\nh
omogeneous probability measure on it\, and discuss the quantization\nerro
rs of the measure and $n$-optimal\nsets for $n \\geq 1$\, and the quantiza
tion dimension. Some open\nproblems in the area will be pointed out.\n\nh
ttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1512
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1512
END:VEVENT
BEGIN:VEVENT
SUMMARY:From Calculus to Number Theory:An introduction to the special valu
es of L-functions
DTSTART;VALUE=DATE-TIME:20110728T103000Z
DTEND;VALUE=DATE-TIME:20110728T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1528@cern.ch
DESCRIPTION:An L-function is a function of one complex variable that is at
tached to some interesting arithmeetic or geometric data. The values of su
ch an L-function\, at interesting points\, give structural information abo
ut the data to which it is attached. This talk will be an introduction\, v
ia examples\, to the subject of special values of L-functions. I will begi
n by recalling some classical formulae which one usually encounters in an
advanced course in Calculus. These formulae\, when recast in modern langua
ge\, are the prototypes of special values of L-functions. Starting at an e
lementary level\, I will build up toward classical results of Manin and Sh
imura on the L-functions of modular forms or of automorphic forms on GL(2)
\; but I will present the results in a fashion which admits generalization
s to higher GL(n).\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.
py?confId=1528
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1528
END:VEVENT
BEGIN:VEVENT
SUMMARY:Unitarity of the KZ/Hitchin connection on conformal blocks in gen
us 0
DTSTART;VALUE=DATE-TIME:20110804T103000Z
DTEND;VALUE=DATE-TIME:20110804T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1543@cern.ch
DESCRIPTION:Associated to a (finite dimensional\, simple) Lie algebra\, an
d\na finite set of irreducible representations (and a level)\, there are v
ector\nbundles of conformal blocks on suitable moduli spaces of curves wi
th marked\npoints. These conformal block bundles carry flat projective co
nnections\n(KZ/Hitchin).\n\nWe prove that conformal block bundles in genus
zero (for arbitrary simple\nLie algebras) carry geometrically defined uni
tary metrics (of\nHodge-theoretic origin\, as conjectured by Gawedzki) wh
ich are preserved\nby the KZ/Hitchin connection. Our proof builds upon th
e work of Ramadas\nwho proved this unitarity statement in the case of the
Lie algebra sl(2)\n(and genus zero).\n\nhttps://indico.tifr.res.in/indic
o/conferenceDisplay.py?confId=1543
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1543
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representations of p-adic groups and Hecke algebras
DTSTART;VALUE=DATE-TIME:20110811T103000Z
DTEND;VALUE=DATE-TIME:20110811T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1555@cern.ch
DESCRIPTION:There is a close interplay between representations of p-adic\n
groups\, and those of certain finitely generated associative algebras\,\ns
everal of which are of much current interest. We discuss some of these\nm
atters in this survey.\n\nhttps://indico.tifr.res.in/indico/conferenceDisp
lay.py?confId=1555
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1555
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Baer rings: A module theoretic analogue and related notions '
DTSTART;VALUE=DATE-TIME:20110818T103000Z
DTEND;VALUE=DATE-TIME:20110818T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1592@cern.ch
DESCRIPTION:Kaplansky introduced the notion of a Baer ring in 1955 which h
as\nclose links to $C^*$-algebras and von Neumann algebras. Maeda and Hatt
ori\ngeneralized this notion to that of a Rickart Ring in 1960. A ring is
called\nBaer (right Rickart) if the right annihilator of any subset (singl
e element)\nof $R$ is generated by an idempotent of $R$.\nUsing the endomo
rphism ring of a module\, we recently extended these two\nnotions to a gen
eral module theoretic setting:\nLet $R$ be any ring\, $M$ be an $R$-module
and $S =End_R(M)$. $M$ is said to be\na {\\it Baer module} if the right a
nnihilator in $M$ of any subset of\n$S$ is generated by an idempotent of $
S$. Equivalently\, the left\nannihilator in $S$ of any submodule of $M$ is
generated by an idempotent\nof $S$. The module $M$ is called a {\\it Rick
art module} if the right\nannihilator in $M$ of any single element of $S$
is generated by an\nidempotent of $S$\, equivalently\, $r_M(\\phi)=Ker \\p
hi \\leq^\\oplus\nM$ for every $\\phi$ in $S$. In this talk we will compar
e and contrast\nthe two notions and present their properties. Endomorphism
ringsof these modules \nand their direct sums will be discussed. We will\
npresent some recent developments in this theory including a dual notion.\
n(This is a joint work with Gangyong Lee and Cosmin Roman.)\n\nhttps://ind
ico.tifr.res.in/indico/conferenceDisplay.py?confId=1592
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1592
END:VEVENT
BEGIN:VEVENT
SUMMARY:What is an Algebraic stack ?
DTSTART;VALUE=DATE-TIME:20110823T090000Z
DTEND;VALUE=DATE-TIME:20110823T100000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1610@cern.ch
DESCRIPTION:This will be an overview of stacks and algebraic stacks\, assu
ming \nnothing more than\nfamiliarity with some elementary notions in alge
braic geometry (as\ndiscussed\, for example\, in undergraduate or first ye
ar graduate courses).\n\nAlgebraic stacks have become important in recent
years due to their\napplications\nin various fields ranging from mathemati
cal physics to the geometric\nLanglands' program. In this talk we will fir
st try to motivate the use of \nstacks\, by considering a few basic exampl
es. After some basic definitions\, \nwe will review how to define various
cohomology-homology theories for \nalgebraic stacks and conclude with some
notable results on algebraic \nstacks.\n\nhttps://indico.tifr.res.in/indi
co/conferenceDisplay.py?confId=1610
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1610
END:VEVENT
BEGIN:VEVENT
SUMMARY:On main conjectures in non-commutative Iwasawa Theory
DTSTART;VALUE=DATE-TIME:20110825T103000Z
DTEND;VALUE=DATE-TIME:20110825T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1612@cern.ch
DESCRIPTION:Recently the main conjecture of non-commutative Iwasawa theory
for totally \nreal fields was proven under the assumption of vanishing of
certain\n$\\mu$ invariant. The proof reduces the non-commutative main con
jecture\nto a family commutative main conjecture (which are known due to W
iles) and \ncertain congruences between special values of Artin $L$-functi
ons (which\nare proven using the Deligne-Ribet $q$-expansion principle). M
ore\ngenerally\, one can reduce non-commutative main conjectures (for any
\nmotive) to commutative main conjectures and certain congruences between\
nspecial values of $L$-functions of Artin twists of the motive. This is\nu
sually referred to as the strategy of Burns-Kato. I will present a \nformu
lation of the non-commutative main conjecture and the strategy of \nBurns-
Kato. The construction of non-commutative $p$-adic $L$-function and the\np
roof of non-commutative main conjecture go hand in hand in the Burns-Kato
\nstrategy. But now we know enough about $K_1$ of Iwasawa algebras to \nco
nstruct non-commutative $p$-adic $L$-functions by just proving certain \nc
ongruences (the {\\it non-commutative Kummer congruences}) between special
\nvalues of $L$-functions.\n\nhttps://indico.tifr.res.in/indico/conferenc
eDisplay.py?confId=1612
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1612
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lipschitz Isometric Maps for Pairs of Riemannian Metrics
DTSTART;VALUE=DATE-TIME:20110908T103000Z
DTEND;VALUE=DATE-TIME:20110908T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1635@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
1635
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1635
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representing hermitian K-theory by orthogonal Grassmannian in A^1-
homotopy theory
DTSTART;VALUE=DATE-TIME:20110915T103000Z
DTEND;VALUE=DATE-TIME:20110915T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1647@cern.ch
DESCRIPTION:In this talk I will explain a joint work with Marco\nSchlichti
ng on geometric representability of hermitian $K$-theory in the\nhomotopy
theory of schemes. After recalling some basic notions from the\nhomotopy t
heory of schemes developed by Morel and Voevodsky\, I will define\nan ind-
scheme $GrO$\, the orthogonal Grassmannian\, and construct a map from\n$Gr
O$ into hermitian $K$-theory $KO$. I will sketch a proof that this map is
a\nhomotopy equivalence and discuss some applications of the result.\n\nht
tps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1647
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1647
END:VEVENT
BEGIN:VEVENT
SUMMARY:Towards the rational homotopy type of moduli stacks of G-bundles o
n curves
DTSTART;VALUE=DATE-TIME:20110922T103000Z
DTEND;VALUE=DATE-TIME:20110922T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1690@cern.ch
DESCRIPTION:We will discuss some ideas on how to determine the rational\nh
omotopy type\nof some moduli stacks of principal $G$-bundles on an algebra
ic curve over\nthe complex\nnumbers. This relies on a good notion of homot
opy types of associated\ntopological stacks\nand an analysis of the Haefli
ger-Brown-Szarba model for the rational\nhomotopy type\nof mapping spaces.
This is work in progress with U. Bujis (Barcelona).\n\nhttps://indico.tif
r.res.in/indico/conferenceDisplay.py?confId=1690
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1690
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fine Selmer group of Hida deformations
DTSTART;VALUE=DATE-TIME:20110929T103000Z
DTEND;VALUE=DATE-TIME:20110929T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1709@cern.ch
DESCRIPTION:Fine Selmer group of an elliptic curve is an arithmetic modu
le which\nis studied in Iwasawa theory. In this talk\, we will study the
fine\nSelmer groups associated to modular forms and $\\Lambda$-adic forms
.\nThese modules are defined over a $p$-adic Lie extension of a number\nfi
eld.\n\nInspired by some deep classical conjectures of Iwasawa and Greenbe
rg\,\nCoates and Sujatha have proposed certain conjectures regarding the
\nstructure of the fine Selmer group. We will formulate analogues of thes
e\nconjectures in the setting of modular forms and also for $\\Lambda$-ad
ic\nforms. We will relate the structure of the `big' fine Selmer group of
a\n$\\Lambda$-adic form to the fine Selmer groups associated to the\nind
ividual modular forms which are specializations of the $\\Lambda$-adic\nfo
rm. We will also compare the usual Greenberg Selmer groups (resp. fine\nS
elmer group) in a family of congruent modular forms associated to a\n$\\La
mbda$-adic form.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py
?confId=1709
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1709
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Negativity of the first Hilbert coefficient
DTSTART;VALUE=DATE-TIME:20111013T103000Z
DTEND;VALUE=DATE-TIME:20111013T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1728@cern.ch
DESCRIPTION:We present a solution to Vasconelos' negativity conjecture in\
ncertain unmixed quotient of regular local rings by explicit calculation o
f\nHilbert polynomials of all ideals generated by system of parameters.\n\
nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1728
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1728
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non-Abelian Grothendieck Duality and Stable Homotopy
DTSTART;VALUE=DATE-TIME:20111020T103000Z
DTEND;VALUE=DATE-TIME:20111020T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1740@cern.ch
DESCRIPTION:I will give a formulation of Grothendieck duality for derived
algebraic\nstacks. These are ordinary Artin/D-M stacks whose structure she
af can be\nenriched to a sheaf of multiplicative cohomology theories. In o
ur\nformulation\, following Toen\, Vessozi and Lurie\, these objects are\n
$(\\infty\,1)$-topoi equipped with a structure sheaf of $E_{\\infty}$-ring
s.\nThe category of quasi-coherent modules over such derived stacks form\n
symmetric monoidal stable model categories\, which are natural homotopical
\ngeneralizations of abelian categories.\n\nI will relate duality in this
context to certain computational aspects of\nstable homotopy theory. It is
common to have generalized cohomology\ntheories arise as homotopy global
sections of certain derived stacks.\nExamples of these are the theory of t
opological modular forms\, real\n$K$-theory\, real Morava E-theories and s
table homotopy itself. Computing the\ncoefficient rings of these theories
involve computing Ext in a category of\ncomodules over a Hopf algebroid\,
which is like a stacky version of group\ncohomology. The associated ordina
ry Tate cohomology object can be\ninterpreted concretely in terms of deriv
ed duality.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?conf
Id=1740
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1740
END:VEVENT
BEGIN:VEVENT
SUMMARY:Betti bounds of polynomials
DTSTART;VALUE=DATE-TIME:20111103T103000Z
DTEND;VALUE=DATE-TIME:20111103T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1753@cern.ch
DESCRIPTION:We initiate a classification of polynomial functions \n$f : {\
\mathbb C}^n \\to {\\mathbb C}$ of degree d having\nthe top Betti number
of the general fibre close to the maximum.\nWe find a range in which the p
olynomial must have isolated\nsingularities and\nanother range where it ma
y have at most one line singularity of\nMorse transversal type. Our method
uses deformations into\nparticular pencils with non-isolated singulariti
es. This is a\njoint work with Dirk Siersma.\n\nhttps://indico.tifr.res.in
/indico/conferenceDisplay.py?confId=1753
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1753
END:VEVENT
BEGIN:VEVENT
SUMMARY:Residues of Intertwining Operators for Classical Groups
DTSTART;VALUE=DATE-TIME:20111117T103000Z
DTEND;VALUE=DATE-TIME:20111117T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1779@cern.ch
DESCRIPTION:Let G be a classical group over a p-adic field.\nRepresentatio
ns of G can be obtained by parabolic induction from Levi\nsubgroups of G.
Such representations are related by ``meromorphic"\nintertwining operator
s. Shahidi observed that these operators encode\ninteresting arithmetic i
nformation. We discuss joint work with\nShahidi in which we employ harmon
ic analysis to detect the presence of\na pole.\n\nhttps://indico.tifr.res.
in/indico/conferenceDisplay.py?confId=1779
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1779
END:VEVENT
BEGIN:VEVENT
SUMMARY:Langlands Functoriality and Howe Correspondences: An Introduction
and Some Examples
DTSTART;VALUE=DATE-TIME:20111124T103000Z
DTEND;VALUE=DATE-TIME:20111124T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1787@cern.ch
DESCRIPTION:Functoriality and theta (Howe) correspondences are common meth
ods used to\nconstruct the representations that arise in the theory of aut
omorphic forms.\nComparing these methods can lead to striking examples wit
h implications for\nnumber theory. In this talk I will give an introductio
n to functoriality and\ntheta-correspondences and then look at some exampl
es of how the methods\ncompare.\n\nhttps://indico.tifr.res.in/indico/confe
renceDisplay.py?confId=1787
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1787
END:VEVENT
BEGIN:VEVENT
SUMMARY:Higgs pairs and the Hitchin map
DTSTART;VALUE=DATE-TIME:20111201T103000Z
DTEND;VALUE=DATE-TIME:20111201T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1813@cern.ch
DESCRIPTION:The abstract will be provided later.\n\nhttps://indico.tifr.re
s.in/indico/conferenceDisplay.py?confId=1813
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1813
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Mathematical Legacy of Srinivasa Ramanujan
DTSTART;VALUE=DATE-TIME:20111208T103000Z
DTEND;VALUE=DATE-TIME:20111208T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1841@cern.ch
DESCRIPTION:The Indian mathematician\, Srinivasa Ramanujan was largely\nse
lf-taught and emerged from extreme poverty to become one of 20th\ncentury'
s influential mathematicians. In this talk\, I will give\na panoramic vie
w of his essential contributions and how they are shaping\nmathematics of
this century.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?co
nfId=1841
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1841
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reflections of a mathematician about the trends of this science in
the past sixty years
DTSTART;VALUE=DATE-TIME:20111212T103000Z
DTEND;VALUE=DATE-TIME:20111212T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1856@cern.ch
DESCRIPTION:There is no abstract. (This is a \nspecial mathematics colloqu
ium)\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1856
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1856
END:VEVENT
BEGIN:VEVENT
SUMMARY:Curvettes and Jacobian Problem
DTSTART;VALUE=DATE-TIME:20111215T103000Z
DTEND;VALUE=DATE-TIME:20111215T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1858@cern.ch
DESCRIPTION:Dicritical Divisors are a new tool of attacking the famous\nJa
cobian Problem. Curvettes are a new way of looking at Dicritical Divisors.
\nA Curvette is a snake-like quadratic sequence risiing from the base ring
to\na prime divisors. They induce an approximate factorization of a two v
ariable\npolynomial which may or may not have a jacobian mate.\n\nDicritic
al Divisors reminded me of Spiders in the Marathi Poem\n`EKA KOLIYANE EKAD
A APULE JALE BANDHIYELE....'\nA Curvette reminds me of the Nag-Panchami Ba
j Exihibition in a MANDIR in\nGwalior\nwhere I grew up\, and a curvette-pa
ir is like the NAGAPASHA released by\nIndrajit.\nJust as spiders were join
t work with Ignacio Luengo\,\nsnakes are joint work with Enrique Artal.\n\
nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1858
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1858
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tree-terated integrals and motives related to the fundamental grou
p
DTSTART;VALUE=DATE-TIME:20120119T103000Z
DTEND;VALUE=DATE-TIME:20120119T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1956@cern.ch
DESCRIPTION:I will describe how to associate a motive to a graph labeled b
y\npoints in an algebraic variety. The periods of this motive will be\ngen
eralizations of iterated integrals which in simple cases yield a special\n
class of Shintani zeta functions. When the variety is an affine curve\,\nr
ealizations of the motive will have dimension given by the chromatic\npoly
nomial of the graph applied to the cohomology of the curve. When the\ngrap
h is simply a string with n points\, one gets the motive of the\nfundament
al group ring modulo the (n+1)st power of the augmentation ideal.\n\nhttps
://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1956
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1956
END:VEVENT
BEGIN:VEVENT
SUMMARY:Counting points of homogeneous varieties over finite fields
DTSTART;VALUE=DATE-TIME:20120202T103000Z
DTEND;VALUE=DATE-TIME:20120202T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-1974@cern.ch
DESCRIPTION:Given a system of polynomial equations with integer\ncoefficie
nts\, one may first reduce it modulo any prime p\, and then\ncount the sol
utions over the prime field F_p and larger finite fields.\nThe talk will p
resent some remarkable properties of the resulting\ncounting function\, fi
rst for general systems and then for those where\nthe complex solutions fo
rm a unique orbit under the action of some\nalgebraic group.\n\nhttps://in
dico.tifr.res.in/indico/conferenceDisplay.py?confId=1974
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=1974
END:VEVENT
BEGIN:VEVENT
SUMMARY:Are there kernels of functoriality ?
DTSTART;VALUE=DATE-TIME:20120209T103000Z
DTEND;VALUE=DATE-TIME:20120209T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2002@cern.ch
DESCRIPTION:There is no abstract\n\nhttps://indico.tifr.res.in/indico/conf
erenceDisplay.py?confId=2002
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2002
END:VEVENT
BEGIN:VEVENT
SUMMARY:Knots and Primes
DTSTART;VALUE=DATE-TIME:20120216T103000Z
DTEND;VALUE=DATE-TIME:20120216T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2018@cern.ch
DESCRIPTION:We will discuss the analogies between\n3-dimensional topology
and number theory.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.
py?confId=2018
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2018
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the irreducibility of irreducible characters of simple Lie alge
bras
DTSTART;VALUE=DATE-TIME:20120301T103000Z
DTEND;VALUE=DATE-TIME:20120301T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2055@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
2055
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2055
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the canonical degree of curves on varieties of general type
DTSTART;VALUE=DATE-TIME:20120307T090000Z
DTEND;VALUE=DATE-TIME:20120307T100000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2068@cern.ch
DESCRIPTION:One of the leading conjectures in arithmetic and algebraic\nge
ometry is the Vojta conjecture. The famous abc conjecture is a special\nca
se of it and it implies a precise control of the behavior of algebraic\npo
ints on varieties of general type. Even in the function fields case\,\nalt
hough much more then the number field case is known\, the main conjecture\
nis widely open. I will report on the conjecture and explain how some Shim
ura\nvarieties provide some insight on the conjecture.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=2068
LOCATION:Colaba Campus Lecture Theatre AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2068
END:VEVENT
BEGIN:VEVENT
SUMMARY:Local Non-Archimedean Dynamical Systems in Two Variables
DTSTART;VALUE=DATE-TIME:20120315T103000Z
DTEND;VALUE=DATE-TIME:20120315T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2071@cern.ch
DESCRIPTION:In joint work with Steven Spallone\, we consider locally-conve
rgent\nanalytic mappings over K^{2}\, where K is a non-archimedean field.
\nOur goal is to construct conjugations to polynomial normal forms. In\npa
rticular\, our focus is on so-called `Semi-hyperbolic' dynamical systems.
\nWe give a full formal and analytic classification\, building off earlier
formal \nwork in the complex plane\, and analytic work in the one-dimensi
onal \nnon-archimedean case. The results are in stark contrast to the comp
lex \ncase.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?conf
Id=2071
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2071
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fundamental group of varieties in positive characteristic
DTSTART;VALUE=DATE-TIME:20120322T103000Z
DTEND;VALUE=DATE-TIME:20120322T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2095@cern.ch
DESCRIPTION:The fundamental group is one of the most basic topological inv
ariant\nof a space. In this talk we will discuss various notions of\nfunda
mental group\, like Grothendieck's etale fundamental group\, Nori's\nfunda
mental group scheme\, the $S$-fundamental group scheme\, etc. which\nmake
sense for varieties over arbitrary fields. We will discuss\nproperties lik
e birational invariance of the $S$-fundamental group\nscheme (joint work w
ith Vikram Mehta).\nWe will also see introduce a new notion of fundamental
group called\n'$\\infty$-stratified fundamental group scheme' (joint work
with\nH\\'el\\`ene Esnault) and its relation with other existing notions
of\nfundamental group.\n\nhttps://indico.tifr.res.in/indico/conferenceDisp
lay.py?confId=2095
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2095
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fourier restriction theorem on Riemannian symmetric spaces of nonc
ompact type
DTSTART;VALUE=DATE-TIME:20120419T103000Z
DTEND;VALUE=DATE-TIME:20120419T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2140@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
2140
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2140
END:VEVENT
BEGIN:VEVENT
SUMMARY:Integrable modules for a Lie Torus
DTSTART;VALUE=DATE-TIME:20120426T103000Z
DTEND;VALUE=DATE-TIME:20120426T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2152@cern.ch
DESCRIPTION:Lie Tori are multivariable generalization of affine Kac-Moody
\nLie algebras. They play an important role in the theory of extended\naff
ine Lie algebras. In this talk we classify irreducible integrable\nmodules
for Lie Torus.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?
confId=2152
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2152
END:VEVENT
BEGIN:VEVENT
SUMMARY:Equivariant K-theory of flag varieties
DTSTART;VALUE=DATE-TIME:20120503T103000Z
DTEND;VALUE=DATE-TIME:20120503T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2180@cern.ch
DESCRIPTION:We will discuss the T-equivariant K-theory of flag varieties\n
G/B\, where G is a semisimple complex algebraic group\, B is a Borel\nsubg
roup and T is a maximal torus in B. The equivariant K-theory of G/B\ncome
s equipped with two natural bases: one coming from the structure\nsheaves
of the Schubert varieties and the other its `dual' basis. We will\nprove s
ome positivity phenomenon in the T-equivariant K-theory of G/B for\nthe pr
oduct structure constants in either of the above two bases. We will\nalso
discuss a generalization of these results to the flag varieties of\nKac-Mo
ody groups.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?conf
Id=2180
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2180
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bundles with negatively curved fibres
DTSTART;VALUE=DATE-TIME:20120507T104500Z
DTEND;VALUE=DATE-TIME:20120507T114500Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2198@cern.ch
DESCRIPTION:This talk is a report on joint work with Pedro Ontaneda. Let M
be\na closed smooth manifold which can support a Riemannian metric with\n
sectional curvatures all negative: e.g. a hyperbolic metric. We are\ninter
ested in smooth M-bundles p:E \\to B whose abstract fiber is M\; \nbut all
of\nwhose specific fibers p^{-1}(x)\, x in B\, are equipped with negative
ly \ncurved\nRiemannian metrics b_x\, which vary continuously with x.\nThi
s is called a bundle with negatively curved fibers. We analyze the\nforget
extra structure map from bundles with negatively curved fibers M to smoot
h M-bundles.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?con
fId=2198
LOCATION:Colaba Campus Lecture Threatre AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2198
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pfaffian representations of quintics
DTSTART;VALUE=DATE-TIME:20120510T103000Z
DTEND;VALUE=DATE-TIME:20120510T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2200@cern.ch
DESCRIPTION:It is known that a general quintic (homogeneous form of degree
\nfive) in five variables can be expressed as the Pfaffian of a\nskew-symm
etric matrix in only finitely many ways upto equivalence. I will\ndiscuss
attempts at finding this number. This is joint work with A.\nPrabhakar Rao
.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2200
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2200
END:VEVENT
BEGIN:VEVENT
SUMMARY:Smooth and Hodge filtered cohomology theories
DTSTART;VALUE=DATE-TIME:20120531T103000Z
DTEND;VALUE=DATE-TIME:20120531T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2278@cern.ch
DESCRIPTION:Smooth cohomology theories are generalized cohomology\ntheorie
s defined for smooth manifolds and have applications in string\ntheory.
Hodge filtered cohomology theories are the analogue for\nholomorphic manif
olds\, and have potential applications to the study of\nalgebraic cycles.
This lecture will describe these cohomology\ntheories and some of thei
r applications.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?
confId=2278
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2278
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algebraic Functions and Analytic Functions
DTSTART;VALUE=DATE-TIME:20120614T103000Z
DTEND;VALUE=DATE-TIME:20120614T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2287@cern.ch
DESCRIPTION:Functions which can be given in terms of polynomials and\nin t
erms of power series are some of the most important functions\nin mathemat
ics. We will look at some of their simple properties\,\nboth local and glo
bal. [This is a VSRP Colloquium].\n\nhttps://indico.tifr.res.in/indico/con
ferenceDisplay.py?confId=2287
LOCATION:Colaba Campus AG-80
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2287
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scissors congruence of polyhedra in Euclidean and Hyperbolic space
s
DTSTART;VALUE=DATE-TIME:20120621T103000Z
DTEND;VALUE=DATE-TIME:20120621T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2291@cern.ch
DESCRIPTION:This is a V.S.R.P. Colloquium. There is no abstract.\n\nhttps:
//indico.tifr.res.in/indico/conferenceDisplay.py?confId=2291
LOCATION:Colaba Campus AG-80
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2291
END:VEVENT
BEGIN:VEVENT
SUMMARY:abc conjecture
DTSTART;VALUE=DATE-TIME:20120628T103000Z
DTEND;VALUE=DATE-TIME:20120628T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2298@cern.ch
DESCRIPTION:There is no abstract. This is a colloquium meant for VSRP stud
ents of\nMaths.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?
confId=2298
LOCATION:Colaba Campus AG-80
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2298
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volumes of hyperbolic 3-manifolds
DTSTART;VALUE=DATE-TIME:20120702T090000Z
DTEND;VALUE=DATE-TIME:20120702T100000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2305@cern.ch
DESCRIPTION:As part of his revolutionary work on hyperbolic geometry in\nt
he 1970's\, Thurston generalizing work of Jorgensen and Gromov\, showed th
at the set of volumes of complete finite volume hyperbolic 3-manifolds is
closed and well ordered. Recently\, Robert Meyerhoff and Peter Milley and
the speaker showed that the Weeks manifold is the unique lowest volume\nc
losed orientable one\, culminating a 30+ year effort by many mathematician
s using a wide variety of geometric and topological techniques. This lect
ure will survey these and other developments and discuss some of the many
open problems in the area.\n\nhttps://indico.tifr.res.in/indico/conference
Display.py?confId=2305
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2305
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the dynamics of holomorphic correspondences on the 2-sphere
DTSTART;VALUE=DATE-TIME:20120705T103000Z
DTEND;VALUE=DATE-TIME:20120705T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2308@cern.ch
DESCRIPTION:We shall look at a couple of equidistribution results for holo
morphic\ncorrespondences on the 2-sphere. Our results have the following\
ncharacter: if F is a holomorphic correspondence on the 2-sphere\, then\,\
nunder certain conditions\, F admits an equilibrium measure \\mu\, and\,\n
for a generic point p in the sphere\, the normalized sums of point\nmasses
carried by the pre-images of p under successive iterates of\nF converge t
o \\mu. Now\, let F^t denote the transpose of F.\nUnder the condition d_{t
op}(F) > d_top(F^t)\, where d_{top} denotes\nthe topological degree\, our
result is a small refinement of a set of\nrecent results by Dinh and Sibon
y. However\, for most interesting\ncorrespondences on the 2-sphere\, d_top
(F) \\leq d_top(F^t). This\nis certainly the case for the correspondences
introduced by Bullett and\nPenrose --- who were among the first to introdu
ce these objects. When\nd_top(F) \\leq d_top(F^t)\, the existence of equil
ibrium measures\,\nand equidistribution results\, seem to depend on whethe
r or not F admits\na repeller. We shall discuss what this means\, and exam
ine some aspects\nof the proof of the relevant equidistribution theorem. T
his is joint\nwork with Shrihari Sridharan.\n\nhttps://indico.tifr.res.in/
indico/conferenceDisplay.py?confId=2308
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2308
END:VEVENT
BEGIN:VEVENT
SUMMARY:The p-adic L-functions of Kubota and Leopoldt
DTSTART;VALUE=DATE-TIME:20120712T103000Z
DTEND;VALUE=DATE-TIME:20120712T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2334@cern.ch
DESCRIPTION:A good part of this talk will be an introduction to the\ntopic
. We will discuss the p-adic analogues of the Riemann zeta function\nand D
irichlet L-functions which were constructed in the early 1960s by\nKubota
and Leopoldt. We also want to discuss a new proof of an old formula\np
roved by Bruce Ferrero and myself in the 1970s. That formula gives\nthe va
lue of the derivative for a Kubota-Leopoldt p-adic L-function\nat s=0 whe
n the function itself vanishes at that point. The new proof\nis a joint p
roject with Benjamin Lundell and Shaowei Zhang and relies on\nstudying a c
ertain anaytic function of two p-adic variables.\n\nhttps://indico.tifr.re
s.in/indico/conferenceDisplay.py?confId=2334
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2334
END:VEVENT
BEGIN:VEVENT
SUMMARY:On locally Laurent polynomial algebras
DTSTART;VALUE=DATE-TIME:20120719T103000Z
DTEND;VALUE=DATE-TIME:20120719T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2345@cern.ch
DESCRIPTION:In 1977\, Bass\, Connell and Wright established that any finit
ely\ngenerated locally polynomial algebra in n variables over an\nintegral
domain R is\nisomorphic to the symmetric algebra of a finitely generated
projective\nR-module of rank n. In this talk\,\nwe shall present an analog
ous structure theorem\nfor any R-algebra which is locally a Laurent polyno
mial\nalgebra in n variables.\n\nNext we shall give sufficient conditions\
nfor a faithfully flat R-algebra A\nto be a locally Laurent polynomial alg
ebra.\nWe shall see that over a discrete valuation ring R any\nLaurent pol
ynomial fibration is necessarily a Laurent\npolynomial algebra. We shall t
hen consider\nfibre conditions over more general domains.\n\nIf time permi
ts\, we shall also mention a few results on\nthe structure of certain alge
bras whose generic\nfibres are {\\mathbb A}^*.\n\nThe results have been ob
tained jointly with S.M. Bhatwadekar.\n\nhttps://indico.tifr.res.in/indico
/conferenceDisplay.py?confId=2345
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2345
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diophantine approximation on varieties
DTSTART;VALUE=DATE-TIME:20120727T100000Z
DTEND;VALUE=DATE-TIME:20120727T110000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2363@cern.ch
DESCRIPTION:I will discuss connections between Diophantine approximation a
nd\nthe ergodic theory of group actions on homogeneous\nspaces with an emp
hasis on recent joint work with Gorodnik and Nevo.\n\nhttps://indico.tifr.
res.in/indico/conferenceDisplay.py?confId=2363
LOCATION:Colaba Campus AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2363
END:VEVENT
BEGIN:VEVENT
SUMMARY:Introduction to Arthur's work on classification of automorphic rep
resentations on classical groups
DTSTART;VALUE=DATE-TIME:20120802T103000Z
DTEND;VALUE=DATE-TIME:20120802T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2371@cern.ch
DESCRIPTION:The recent work of Arthur on classification of automorphic\nre
presentations on classical groups is a landmark result in the Langlands'\n
program. In this talk we will try to indicate the nature of the\nclassific
ation and the tools that are used in the proof.\n\nhttps://indico.tifr.res
.in/indico/conferenceDisplay.py?confId=2371
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2371
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algebraic cobordism and algebraic equivalence
DTSTART;VALUE=DATE-TIME:20120809T103000Z
DTEND;VALUE=DATE-TIME:20120809T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2387@cern.ch
DESCRIPTION:There is no abstract.\n\nhttps://indico.tifr.res.in/indico/con
ferenceDisplay.py?confId=2387
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2387
END:VEVENT
BEGIN:VEVENT
SUMMARY:Period-index problem for the Brauer group
DTSTART;VALUE=DATE-TIME:20120814T103000Z
DTEND;VALUE=DATE-TIME:20120814T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2393@cern.ch
DESCRIPTION:Class field theory leads to period=index for finite dimension
al division\nalgebras over number fields. There are open questions concern
ing bounding the index of algebras in terms of their period for fields fin
itely generated fields over prime fields. We shall explain how such bounds
would lead to nontrivial consequences for the existence of rational point
s on quadrics.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?c
onfId=2393
LOCATION:Colaba Campus AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2393
END:VEVENT
BEGIN:VEVENT
SUMMARY:Finiteness for the Module Structure of a Group Action on a Polynom
ial Ring
DTSTART;VALUE=DATE-TIME:20120816T103000Z
DTEND;VALUE=DATE-TIME:20120816T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2394@cern.ch
DESCRIPTION:A finite group typically has infinitely many isomorphism class
es of\nindecomposable modular representations. We show that from a polyno
mial\nring (i. e. symmetric algebra of a single representation) one can ob
tain\nonly finitely many isomorphism classes of indecomposables.\n\nThis i
s the main theorem of the speaker's paper with Peter Symonds.\n\nhttps://i
ndico.tifr.res.in/indico/conferenceDisplay.py?confId=2394
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2394
END:VEVENT
BEGIN:VEVENT
SUMMARY:Residual Albanese quotients of Picard modular surfaces\, and ratio
nal points
DTSTART;VALUE=DATE-TIME:20120830T103000Z
DTEND;VALUE=DATE-TIME:20120830T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2420@cern.ch
DESCRIPTION:A well known result of Mazur shows the paucity of rational poi
nts outside\nthe cusps on modular curves of high genus. This talk will pre
sent a program with M. Dimitrov to try to establish a weak analogue for th
e Picard modular surfaces X\, which arise as quotients of the unit ball in
C^2 by congruence subgroups of U(2\,1) associated to an imaginary quadrat
ic field E. It is\nknown that the Albanese variety of any such X is of CM
type. A key role for us will be played by the part of Alb(X) coming from
residual automorphic forms on U(2\,1). The presentation will be concrete\
, presenting examples of residual quotients A of finite Mordell-Weil group
\, and will investigate consequences for the arithmetic on X.\n\nhttps://i
ndico.tifr.res.in/indico/conferenceDisplay.py?confId=2420
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2420
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Spectrum of tensor triangulated catgories
DTSTART;VALUE=DATE-TIME:20120906T103000Z
DTEND;VALUE=DATE-TIME:20120906T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2437@cern.ch
DESCRIPTION:P. Balmer introduced the notion of spectrum of tensor\ntriangu
lated categories to extract geometric information from the\ncategorical d
ata. One of problem in this direction is to compute\nspectrum for various
examples.\n \nIn this talk we present some examples coming from Algebraic
Geometry.\nWe'll first briefly recall tensor triangulated categories and
then we'll\ngive basic definitions related to spectrum. We'll also indicat
e the Balmer's method of reconstruction of certain schemes using spectrum.
\n\nIf time permit we'll indicate proof of results obtained with Vivek M.\
nMallick.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId
=2437
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2437
END:VEVENT
BEGIN:VEVENT
SUMMARY:Weightless Cohomology of Algebraic Varieties
DTSTART;VALUE=DATE-TIME:20120913T103000Z
DTEND;VALUE=DATE-TIME:20120913T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2453@cern.ch
DESCRIPTION:We construct a new functorial cohomology theory on the\ncatego
ry of varieties over a base field k using mixed hodge modules of\nSaito
(if k is complex numbers) or Frobenius weights (if k \nis finite). The
construction is motivic and naturally arises in the context of Shimura Var
ieties where it captures the cohomology of Reductive Borel Serre compactif
ication.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
2453
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2453
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Tate conjecture for K3 surfaces over fields of odd characteri
stic
DTSTART;VALUE=DATE-TIME:20120920T103000Z
DTEND;VALUE=DATE-TIME:20120920T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2464@cern.ch
DESCRIPTION:Using the theory of integral canonical models of\nShimura vari
eties (due to Faltings-Kisin-Vasiu)\, we extend the classical\nKuga-Satake
construction for\nK3 surfaces over fields of odd characteristic. This con
struction attaches to every polarized K3 surface X an abelian variety A\,\
nand allows us (always when p>3\; in certain cases when p=3) to identify t
he Picard group of X with\na certain space of endomorphisms (called 'speci
al endomorphisms') of A.\nUsing new results of Kisin towards a proof of th
e Langlands-Rapoport\nconjecture\, we can now reduce the Tate conjecture\n
for X to the Tate conjecture\nfor endomorphisms of A\, which is already kn
own due to Tate and\nZarhin. Over finite fields of characteristic at least
5\, the Tate conjecture for K3 surfaces is already known by work of Nygaa
rd-Ogus\, Maulik and Charles\, but our proof is uniform and works also\nov
er infinite\, finitely generated fields.\n\nhttps://indico.tifr.res.in/ind
ico/conferenceDisplay.py?confId=2464
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2464
END:VEVENT
BEGIN:VEVENT
SUMMARY:On a hidden property of Borcherds products
DTSTART;VALUE=DATE-TIME:20120927T103000Z
DTEND;VALUE=DATE-TIME:20120927T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2471@cern.ch
DESCRIPTION:Borcherds products are special automorphic forms for the ortho
gonal\ngroup $O_{2\,n}(\\R)$ of signature $(2\,n)$\, lifts from weakly mo
dular\nforms. To state explicit examples we identify $O_{2\,2}$ with $SL_2
\n\\times SL_2$ and $O_{2\,3}$ with the Siegel modular group of degree\n$2
$.\n\nLet $j$ be the modular invariant with Fourier coefficients $c(n)$\,\
nnormalized with $c(0)=0$. Then one of the most famous examples is\ngiven
by\n\n$$j(z)-j(w) = p^{-1} \\prod_{m=1\, n\\geq -1}^{\\infty} \\left( 1 -
p^m q^n\\right)^{c(nm)} \n\\quad \\left(p:=e^{2 \\pi i z}\, q:=e^{2 \\pi
i w}\\right)\, $$\n\nrelated to the denominator formula of the monster Lie
algebra. This\nformula had been known before by Koike\, Zagier. New was t
he link to\nthe Moonshine conjecture and a systematic\nconstruction of aut
omorphic products called Borcherds lifts due to\nBorcherds.\nThe case\nof
Siegel modular forms has been first studied by Gritsenko and\nNikulin. The
y found a deep connection between the Igusa function\n$\\Delta_5$ and a ce
rtain Kac-Moody algebra with implications in\nrepresentation theory. Borch
erds proved that the lifts have Heegner\ndivisors\, and conversely Bruinie
r proved that in principle every\nmodular form with Heegner divisors is a
Borcherds lift. \nSince modular\nforms are usually given by Fourier expans
ion (for example Eisenstein\nseries\, Theta series\, Maass lifts) it is no
t easy to decide if a\nconcrete given form is a Borcherds lift. \n\nRecent
ly we discovered a\nhidden property of Borcherds lifts giving a complete\n
characterization. In this talk we describe the property\, sketch the\nproo
f and give applications. This is a joint project with Atsushi\nMurase.\n\n
https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2471
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2471
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ray class groups and generalised Jacobians
DTSTART;VALUE=DATE-TIME:20121004T103000Z
DTEND;VALUE=DATE-TIME:20121004T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2494@cern.ch
DESCRIPTION:We will extend Iwasawa's analogy between class groups in\np-cy
clotomic towers and Jacobians of curves to ray class groups in\ncyclotomic
towers and generalised Jacobians\, and explain how a\nwell-known conjectu
re of Leopoldt about p-adic independence of units\nfits into this context.
This is part of a joint work with\nWintenberger.\n\nhttps://indico.tifr.r
es.in/indico/conferenceDisplay.py?confId=2494
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2494
END:VEVENT
BEGIN:VEVENT
SUMMARY:Poncelet porism and elliptical billiards
DTSTART;VALUE=DATE-TIME:20121011T103000Z
DTEND;VALUE=DATE-TIME:20121011T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2502@cern.ch
DESCRIPTION:Suppose that two conics are given in the plane\, together with
a\nclosed polygonal line inscribed\nin one of them and circumscribed abou
t the other one. Then\, Poncelet\nporism states that infinitely many\nsuch
closed polygonal lines exist - every point of the first conic is a\nverte
x of such a polygon.\nIn the talk\, the most important results and ideas a
round Poncelet porism\,\nboth classical and modern\,\ntogether with their
historical origins and natural generalizations will be\npresented. We will
particularly\npay attention to applications in billiard dynamics includin
g\nhigher-dimesional cases.\n\nhttps://indico.tifr.res.in/indico/conferenc
eDisplay.py?confId=2502
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2502
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moment maps\, Yang-Mills functional and vortices
DTSTART;VALUE=DATE-TIME:20121018T103000Z
DTEND;VALUE=DATE-TIME:20121018T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2528@cern.ch
DESCRIPTION:Consider a complex reductive group acting linearly on a non-si
ngular\nvariety. According to the work of Kirwan\, the semistable locus ca
n be\nconsidered the open stratum in the Morse stratification induced by t
he\nsquare of the moment map. If the symplectic quotient exists\, it coinc
ides\nwith the GIT quotient.\n\nThe Narasimhan-Seshadri-Donaldson theorem
is an infinite dimensional version\nof this phenomenon\, with the moment m
ap being the Yang-Mills functional.\nThis theorem relates the space of sem
i-stable holomorphic structures on a\nvector bundle to the space of Hermit
ian-Einstein connections.\n\nSimilar results have also been proved on the
space of holomorphic bundles\nwith some additional data\, for example a ho
lomorphic section. In this case\,\nsetting the moment map equal to zero gi
ves the vortex equation.\n\nhttps://indico.tifr.res.in/indico/conferenceDi
splay.py?confId=2528
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2528
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rational torsion points of abelian varieties over a large extensio
n of a local field
DTSTART;VALUE=DATE-TIME:20121101T103000Z
DTEND;VALUE=DATE-TIME:20121101T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2541@cern.ch
DESCRIPTION:We extend the following theorem of H. Imai in several ways:\nI
f A is an abelian variety with potentially good reduction\nover a finite
extension K of Q_p\, then it has only\nfinitely many rational torsion p
oints over the maximal\np-cyclotomic extension of K. In particular\, we p
rove\nthe finiteness over K(K^{1/p^\\infty}). It has applications\nin Iwa
sawa theory.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?con
fId=2541
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2541
END:VEVENT
BEGIN:VEVENT
SUMMARY:An analogue of Raynaud's theory in rigid analytic and formal geome
try
DTSTART;VALUE=DATE-TIME:20121108T103000Z
DTEND;VALUE=DATE-TIME:20121108T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2560@cern.ch
DESCRIPTION:In Raynaud's approach to rigid analytic geometry\, rigid\nanal
ytic spaces are interpreted as generic fibres of formal schemes.\nGrosse-K
loenne\, motivated by Berthelot's rigid cohomology\, defined\ndagger space
s as overconvergent analogues of rigid analytic spaces.\nMeredith defined
weak formal schemes using Monsky and Washnitzer's\ndefinition of weak comp
letion of algebras. In a similar vein to\nRaynaud's theory\, we interpret
dagger spaces as generic fibres of weak\nformal schemes and establish a pr
ecise relationship between them.\n\nhttps://indico.tifr.res.in/indico/conf
erenceDisplay.py?confId=2560
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2560
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Self-dual representations with vectors fixed under an Iwahori sub
group'
DTSTART;VALUE=DATE-TIME:20121122T103000Z
DTEND;VALUE=DATE-TIME:20121122T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2579@cern.ch
DESCRIPTION:An irreducible smooth self-dual representation of a reductive
$p$-adic group preserves either a non-zero symmetric or a nonzero \naltern
ating form on the underlying space and accordingly is said to have sign pl
us one or minus one. There is strong evidence \nthat this sign is always o
ne in the case of representations with non-trivial Iwahori fixed vectors.
We will discuss some of this \nevidence.\n\nhttps://indico.tifr.res.in/ind
ico/conferenceDisplay.py?confId=2579
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2579
END:VEVENT
BEGIN:VEVENT
SUMMARY:Complex Structures on Product of Circle Bundles over Compact Compl
ex Manifolds.
DTSTART;VALUE=DATE-TIME:20121129T103000Z
DTEND;VALUE=DATE-TIME:20121129T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2611@cern.ch
DESCRIPTION:Abstract:\nLet $L_i \\rightarrow X_i$ be holomorphic line bun
dle over \ncompact complex manifold $X_i$\, for $i = 1\,2$. With respect t
o any\nhermitian inner product over $L_i$\, we denote the associated circl
e bundle\nby $S(L_i)$. The aim of this talk is to describe a family of com
plex\nstructures on $S(L_1) \\times S(L_2)$. As a special case when $X_i$
are\nprojective space $\\mathbb P^{n_i}$ and the line bundles are tautolog
ical\nline bundles\, Calabi-Eckmann obtained a family of complex structu
res on\nthe product of odd dimensional spheres\, $S^{2n_1 +1} \\times S^{2
n_2 +1}$.\nLater Loeb and Nicolau constructed a more general family of com
plex\nstructures on $S^{2n_1+1} \\times S^{2n_2 +1}$. We generalize the\
nLoeb-Nicolau construction to obtain the complex structures on $S(L_1)\n\
\times S(L_2)$. These complex manifolds will be non-K\\"{a}hler. This is\n
joint work with Prof P.Sankaran.\n\nhttps://indico.tifr.res.in/indico/conf
erenceDisplay.py?confId=2611
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2611
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Low Dimensional Projective Groups'
DTSTART;VALUE=DATE-TIME:20121205T103000Z
DTEND;VALUE=DATE-TIME:20121205T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2626@cern.ch
DESCRIPTION:ABSTRACT :-\n\nWe shall discuss some recent progress towards t
he conjecture that\nif the fundamental group G of a compact projective man
ifold has\ncohomological dimension less than 4\, it must be the fundamenta
l group of a\nRiemann surface.\n\nSample theorems include:\na) Let $1 -> N
-> G -> Q -> 1$ be an exact sequence of finitely presented\ngroups\, wher
e $Q$ is infinite and not virtually\ncyclic\, and is the fundamental group
of some closed 3-manifold.\nIf $G$ is Kahler\, we show that $Q$ contains
as a finite index subgroup\neither a finite index subgroup of the 3-dimens
ional Heisenberg group or the\nfundamental group of the Cartesian product
of a closed oriented surface of\npositive genus and the circle.\nIt follow
s that no infinite 3-manifold group can be Kaehler(originally\nproved by D
imca and Suciu).\n\nb) If $G$ is a one-relator group\, it must be the fund
amental group of a\nRiemann surface.\n\nc) If $G$ has cohomological dimens
ion 2\, then modulo the Shafarevich\nconjecture\, it must be the fundament
al group of a Riemann surface.\n(This is joint work with Indranil Biswas a
nd Harish Seshadri)\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay
.py?confId=2626
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2626
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dual reductive pairs\, and Exceptional Lie groups
DTSTART;VALUE=DATE-TIME:20121213T103000Z
DTEND;VALUE=DATE-TIME:20121213T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2638@cern.ch
DESCRIPTION:ABSTRACT: \n\nDual reductive pairs are important algebraic obj
ects in\nrepresentation theory of p-adic groups.\nThese were studied by Ro
ger Howe for the symplectic group\, and through the\nWeil representation o
f the symplectic group\, play an important role in the\nsubject.\nIn this
lecture\, we classify dual reductive pairs in all excetional Lie\ngroups.
As a step in this\ndirection\, we also discuss classification of exception
al Lie groups over\ngeneral fields in terms of Octonion and Jordan algebr
as\, and then use\nHasse principle for Galois cohomology to classify them
over number fields.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay
.py?confId=2638
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2638
END:VEVENT
BEGIN:VEVENT
SUMMARY:Automorphisms of positive entropy on compact Kahler or algebraic v
arieties
DTSTART;VALUE=DATE-TIME:20121227T103000Z
DTEND;VALUE=DATE-TIME:20121227T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2666@cern.ch
DESCRIPTION:ABSTRACT:\n\nAn automorphism g on a compact variety X is of po
sitive entropy if\nits action on the cohomology groups of X is of expandin
g type.\nWe report recent results on the relation between the geometry of
X and\nthe existence of such expanding g and characterise those X with a m
aximal\nnumber of such g of expanding type.\n\nhttps://indico.tifr.res.in/
indico/conferenceDisplay.py?confId=2666
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2666
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algebraic hypergeometric functions
DTSTART;VALUE=DATE-TIME:20130214T103000Z
DTEND;VALUE=DATE-TIME:20130214T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2771@cern.ch
DESCRIPTION:\n ABSTRACT: In this lecture we start with the classical hyper
geometric function studied by Gauss. A classical result by H.A.Schwarz giv
es a classification of all such functions which are at the same time algbr
aic functions. We will discuss extensions of this result to the several va
riable case\, known as A-hypergeometric functions\, defined around 1989 by
Gel'fand\, Kapranov and Zelevinsky.\n\nhttps://indico.tifr.res.in/indico/
conferenceDisplay.py?confId=2771
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2771
END:VEVENT
BEGIN:VEVENT
SUMMARY:Harmonic analysis on classical p-adic groups and L-packets
DTSTART;VALUE=DATE-TIME:20130219T103000Z
DTEND;VALUE=DATE-TIME:20130219T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2779@cern.ch
DESCRIPTION:ABSTRACT\nLocal Langlands correspondences for reductive groups
generalise\nthe Artin reciprocity law from the local class field theory.
These\ncorrespondences are expected to give natural partitions of irreduci
ble\nrepresentations into finite sets\, called L-packets. There were recen
tly\nbig breakthroughs regarding them in the case of classical p-adic grou
ps\n(other then GL-groups which were settled earlier).\n\nFrom the other s
ide\, the square integrable packets emerge naturally\nconsidering some ver
y basic problems of (pure) harmonic analysis of these groups.\n\nIn our le
cture we shall discuss this connection\, and how crucial data of\none theo
ry correspond to the crucial data of the other theory (this is\nnice insta
nce of unity which we sometimes meet in mathematics). We shall\ndiscuss ho
w one can describe elements of packets and related questions\,\nlike for e
xample\, given an irreducible square integrable representation\, what are
the other elements of the packet etc.. All this is directly related to th
e classification of tempered representations and non-unitary dual in terms
of cuspidal representations. Such classification in the case of GL-groups
is given by Bernstein-Zelevinsly theory.\n\nThe other topic that we shall
discuss in the lectures is the\nunitarizability problem for classical gro
ups. We recall that soon after\ncompletion of Bernstein-Zelevinsky theory\
, the unitary duals in the\nGL-case were classified (giving the same answe
r in the archimedean case). We expect pretty explicit picture of the unita
ry duals of classical groups\, although much more complicated then in the
GL-case (recall that similarly the classification of the irreducible squar
e integrable representations is substantially more complicated for these g
roups then for GL-groups). For getting the answer\, several difficult ques
tions remains to be settled. We shall discuss what shape of classification
we can expect and possible strategy for solving the problem.\n\nhttps://i
ndico.tifr.res.in/indico/conferenceDisplay.py?confId=2779
LOCATION:Colaba Campus AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2779
END:VEVENT
BEGIN:VEVENT
SUMMARY:WHAT IS K-THEORY AND WHAT IS IT GOOD FOR ?
DTSTART;VALUE=DATE-TIME:20130228T103000Z
DTEND;VALUE=DATE-TIME:20130228T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2810@cern.ch
DESCRIPTION:This talk consists of four points.\n\n1. The basic definition
of K-theory\n\n2. A brief history of K-theory\n\n3. Algebraic versus topo
logical K-theory\n\n4. The unity of K-theory\n\nThe talk is intended for n
on-specialists. Only a general mathematical\nbackground will be assumed.\n
\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2810
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2810
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cornelius Lanczos' mysterious formula for the Gamma function
DTSTART;VALUE=DATE-TIME:20130307T103000Z
DTEND;VALUE=DATE-TIME:20130307T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2817@cern.ch
DESCRIPTION:In 1964\, Cornelius Lanczos proposed entirely without proof a
new kind of asymptotic expansion of the Gamma function\, very different fr
om tirling's formula and much more mysterious. In his 2004 UBC thesis a fo
rmer student of mine\, Glen Pugh\, derived Lanczos' formula and uncovered
some of the most peculiar phenomena I have ever seen in the behaviour of a
symptotic expansions. I am not aware that anyone has explained rigourousl
y what is going on.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay
.py?confId=2817
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2817
END:VEVENT
BEGIN:VEVENT
SUMMARY:HOLONOMY GROUP SCHEME OF AN INTEGRAL CURVE
DTSTART;VALUE=DATE-TIME:20130314T103000Z
DTEND;VALUE=DATE-TIME:20130314T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2837@cern.ch
DESCRIPTION:I will describe the 'HOLONOMY GROUP' of smooth curves and smo
oth \nprojective varieties as a generalization of Fundamental Group. Thi
s was carried out in the past jointly with Indrani Biswas\, S. Subramanian
and V. Balaji through a series of papers. Then we define it for integral
curves. Then we explain the relation between (strongly) stable bundles an
d irreducible representations of these groups.\n\nThis is a joint work Us
ha Bhosle. Recently\, with Usha Bhosle and Sanjay Sigh\, it was further g
eneralized to Hitchin pairs on an integral curve and defined a more genera
l Holonomy groups.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.
py?confId=2837
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2837
END:VEVENT
BEGIN:VEVENT
SUMMARY:D-modules on a class of G-representations
DTSTART;VALUE=DATE-TIME:20130418T103000Z
DTEND;VALUE=DATE-TIME:20130418T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2914@cern.ch
DESCRIPTION:We give an answer to abstract Capelli problem:\nLet (G\, V) be
a multiplicity free finite dimensional representation\nof a connected red
uctive complex Lie group G and G' be its derived\nsubgroup. Assume that th
e categorical quotient V//G is one dimensional\,\ni.e.\, there exists a po
lynomial f generating the algebra of G'-invariant\npolynomials on V (\\C[V
]^G' = \\C[f]) and such that f \\not\\in \\C[V]^G ).\nWe prove that the ca
tegory of regular holonomic D_V-modules invariant\nunder the action of G i
s equivalent to the category of graded modules\nof finite type over a suit
able algebra.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?co
nfId=2914
LOCATION:Colaba Campus A-369
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2914
END:VEVENT
BEGIN:VEVENT
SUMMARY:A theorem of G\\"ollnitz and its place in the theory of partitions
DTSTART;VALUE=DATE-TIME:20130523T103000Z
DTEND;VALUE=DATE-TIME:20130523T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-2997@cern.ch
DESCRIPTION:ABSTRACT\n\nA Rogers-Ramanujan (R-R) type identity is a q-hype
rgeometric identity which is in the form of a series equal to a product\,
with the series representing the generating function of partitions whose p
arts satisfy\ndifference conditions and the product being the generating
function of partitions whose parts satisfy congruence conditions. R-R type
identities arise in a variety of settings ranging from the study of verte
x operators in Lie algebras to exactly solvable models in physics. One of
the deepest\nR-R type identities is a 1967 theorem of G\\"ollnitz. We will
describe a new approach to the G\\"ollnitz theorem using the combinatoric
s of words and view the theorem as emerging from an incredible three para
meter q-hypergeometric identity. As a consequence we get combinatorial ins
ights into Jacobi's triple product identity for theta functions and certai
n partition congruences modulo powers of 2. Companion results to G\\"ollni
tz's theorem can be constructed as well. We will also briefly indicate wha
t lies beyond G\\"ollnitz's theorem in four free parameters.\nThe talk wil
l include joint work with George Andrews\, Basil Gordon\,\nand Alexander B
erkovich.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId
=2997
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=2997
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benford's law
DTSTART;VALUE=DATE-TIME:20130613T103000Z
DTEND;VALUE=DATE-TIME:20130613T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3024@cern.ch
DESCRIPTION:ABSTRACT\nBenford's law describes the distribution of the firs
t digit in many\nnaturally occurring data sets and integer sequences. In t
his talk\, we\ndiscuss this phenomenon and some of its applications.\n\nht
tps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3024
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3024
END:VEVENT
BEGIN:VEVENT
SUMMARY:A finite combinatorial presentation for closed smooth manifolds
DTSTART;VALUE=DATE-TIME:20130709T210000Z
DTEND;VALUE=DATE-TIME:20130709T220000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3074@cern.ch
DESCRIPTION:I will define a class of finite simplicial n-complexes K simpl
exwise linearly embedded in \\R^{n+s} such that\, by a well defined smooth
ing process\, K inherits from \\R^{n+s} a smooth submanifold structure tha
t is well defined up to concordance in the sense of M. Hirsch. Every\nclos
ed smooth n-submanifold of \\R^{n+s} is so presented. Ideas of S.Cairns an
d J.H.C. Whitehead are used.\n\nIn 1991\, Macpherson conjectured a quite d
ifferent finite combinatorial presentation for closed smooth manifolds\; i
t involves matroids. But the\nbasic question whether it really determines
a smooth structure up to diffeomorphism or concordance is (I believe) stil
l open.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3
074
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3074
END:VEVENT
BEGIN:VEVENT
SUMMARY:Higher Multiplicities in Number Theory
DTSTART;VALUE=DATE-TIME:20130711T103000Z
DTEND;VALUE=DATE-TIME:20130711T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3066@cern.ch
DESCRIPTION:ABSTRACT:\nWe will describe interesting interactions between d
ifferent higher\ncongruences\, different notions of derivatives and zeta v
alues\, both in the\nnumber field and the function field situations.\n\nht
tps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3066
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3066
END:VEVENT
BEGIN:VEVENT
SUMMARY:A CLOSER LOOK AT WEIGHT DIAGRAMS
DTSTART;VALUE=DATE-TIME:20130717T223000Z
DTEND;VALUE=DATE-TIME:20130717T233000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3088@cern.ch
DESCRIPTION:The talk presents recent enhancements of the\nrepresentation t
heoretic and geometric methods\nin the study of exceptional groups. In the
\nlectures at TIFR in 2011\, and in the previous\nlectures this week in th
e framework \nATM Workshop on Classical and Non-stable Algebraic K-Theory\
nI sketched the use of minimal modules\nfor calculations in exceptional gr
oups over\nrings. Essentially\, I explained\, that weight\ndiagrams are an
efficient substitute of matrices\,\nwhen you deal with an individual colu
mn or row\nof a matrix. However\, applications at the level\nof $K_2$ and
more sophisticated applications at\nthe level of $K_1$ require more. I out
line some\nnew results\, which indicate that with the use\nof weight diagr
ams you can do much more\, and\neasily calculate with several columns and/
or\nrows of elements of exceptional groups. I mention\nseveral current or
potential applications\, such\nas stability for $K_1$ and $K_2$\, descript
ion of\nsubnormal subgroups\, overgroups of subsystem\nsubgroups\, structu
re of not necessarily split\nisotropic groups\, etc.\n\nhttps://indico.tif
r.res.in/indico/conferenceDisplay.py?confId=3088
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3088
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Struture of an Unramified $L$-Packet and Related Results
DTSTART;VALUE=DATE-TIME:20130822T103000Z
DTEND;VALUE=DATE-TIME:20130822T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3157@cern.ch
DESCRIPTION:Let $\\mathrm G$ be a connected reductive group over\na nonarc
himedean local field $F$\, such as $\\mathbb{Q}_p$. The local\nLanglands c
onjectures predict that the (isomorphism classes\nof) irreducible `admissi
ble'\nrepresentations of $\\mathrm G(F)$ (in vector spaces over\n$\\mathbb
{C}$) can be partitioned in a certain natural way\ninto equivalence classe
s\, called $L$-packets.\n\nHere we will consider an `unramified'\n$\\mathr
m G$\, and the unramified representations of\n$\\mathrm G(k)$. Such repres
entations can be parameterized\nby pairs $(K\, \\lambda)$\, where $K$ is a
so called\n`hyperspecial' compact subgroup of $\\mathrm G(k)$ and\n$\\lam
bda$ is a character of a maximally split maximal torus\n$\\mathrm T$ of $\
\mathrm G$. Let $\\tau_{K\, \\lambda}$\nbe the representation associated t
o a pair $(K\, \\lambda)$.\n\nWe will first describe when two such represe
ntations\n$\\tau_{K\, \\lambda}$ and $\\tau_{K'\, \\lambda'}$ are isomorph
ic.\nNow given an unramified $L$-packet we can :\n(i) think of its element
s as\n$\\tau_{K\, \\lambda}$ for certain (equivalence classes of)\npairs $
(K\, \\lambda)$\; and\n(ii) realize the set of these elements as a princip
al\nhomogeneous space for a certain natural finite abelian group.\n\nWe wi
ll describe how the parametrization in (ii) is related\nto the description
in (i).\n\n\nIt has been well known for a while that\, using the so calle
d\nSatake isomorphism or otherwise\, one can attach to an unramified repre
sentation of an unramified group $\\mathrm G$\na Frobenius-twisted semisim
ple conjugacy class in the Langlands dual\ngroup $\\hat G$ of $\\mathrm G$
. We will generalize this result to\nan analogous class of representations
of a {\\em tamely ramified}\ngroup $\\mathrm G$. The key step in the proo
f is a description of the\nimage under the local Langlands correspondence
of the set of\ncharacters of a torus that are trivial on its `Iwahori subg
roup'.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=31
57
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3157
END:VEVENT
BEGIN:VEVENT
SUMMARY:The irreducible modules for the derivations of the rational quantu
m torus
DTSTART;VALUE=DATE-TIME:20130905T103000Z
DTEND;VALUE=DATE-TIME:20130905T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3174@cern.ch
DESCRIPTION:Let $\\mathbb{C}_q$ be the quantum torus associated with the $
d\n\\times d$ matrix $q = (q_{ij})$\,\n$q_{ii} = 1$\, $q_{ij}^{-1} = q_{ji
}$\, $q_{ij}$ are roots of unity\, for all\n$1 \\leq i\, j \\leq d$ .\nLet
Der$(\\mathbb{C}_q)$ be the Lie algebra of all the derivations of\n$\\mat
hbb{C}_q$.W.Lin and S.Lan defined a functor from $gl_d$-modules to\nDer$(C
_q)$modules.\nThey proved that for a finite dimensional irreducible $gl_d$
-module $V$\,\n$V \\otimes \\mathbb{C}_q$ is a completely reducible Der$(C
_q)$-module\nexcept finitely many cases. In this talk we will show that $V
\\times\n\\mathbb{C}_q$ is an irreducible Der($\\mathbb{C}_q) \\ltimes\n\
\mathbb{C}_q$-module which satisfies some conditions. The main aim of the\
ntalk is to prove the converse of the above fact i.e.\, if $V'$ is an\nirr
educible $\\mathbb{Z}^d$-graded Der($\\mathbb{C}_q) \\ltimes\n\\mathbb{C}_
q$-module with finite dimensional weight spaces which\nsatisfies some cond
itions\, then $V' \\cong V \\otimes C_q$ as\nDer($\\mathbb{C}_q) \\ltimes
\\mathbb{C}_q$-module and when restricted to\nDer($\\mathbb{C}_q$)\, it is
isomorphic to the module defined by W.Lin and S.Lan.\n\nThis is a joint w
ork with Eswara Rao and Punita Batra.\n\nhttps://indico.tifr.res.in/indico
/conferenceDisplay.py?confId=3174
LOCATION:Colaba Campus
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3174
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bounded hypergeometric functions associated to root systems.
DTSTART;VALUE=DATE-TIME:20130912T103000Z
DTEND;VALUE=DATE-TIME:20130912T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3189@cern.ch
DESCRIPTION:A natural extension of Harish-Chandra's theory of spherical\nf
unctions on Riemannian symmetric spaces of non-compact type was introduced
\nby Heckman and Opdam in the late eighties. In this theory\, the symmetri
c\nspace $G/K$ is replaced with a triple $(\\mathfrak{a}\, \\Sigma\, m)$ w
here\n$\\mathfrak{a}$ is a Euclidean vector space with an inner product\,
$\\Sigma$ a root system in $\\mathfrak{a}^{*}$ and $m$ a multiplicity func
tion on $\\Sigma.$ Associated to this triple\, there is a family of commut
ing differential operators (which coincide with left $G$-invariant differe
ntial operators on $G/K$ when the triple is geometric) which admit joint e
igenfunctions called hypergeometric functions (these functions coincide wi
th Harish-Chandra's spherical functions in the geometric case). We study t
hese functions and characterize the bounded hypergeometric functions\, thu
s establishing an analogue of the celebrated theorem of Helgason and Johns
on. This is joint work with Angela Pasquale and Sanjoy Pusti.\n\nhttps://
indico.tifr.res.in/indico/conferenceDisplay.py?confId=3189
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3189
END:VEVENT
BEGIN:VEVENT
SUMMARY:Combinatorics and algebraic geometry:some examples from toric vari
eties.
DTSTART;VALUE=DATE-TIME:20130919T103000Z
DTEND;VALUE=DATE-TIME:20130919T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3195@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
3195
LOCATION:Colaba Campus
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3195
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moduli spaces of principal bundles on projective varieties
DTSTART;VALUE=DATE-TIME:20131004T023000Z
DTEND;VALUE=DATE-TIME:20131004T033000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3250@cern.ch
DESCRIPTION:ABSTRACT\n\nThe moduli space of principal bundles on curves wa
s constructed by A.\nRamanathan. I will discuss several ideas that have be
en used to generalize\nthis to projective varieties.\n\nhttps://indico.tif
r.res.in/indico/conferenceDisplay.py?confId=3250
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3250
END:VEVENT
BEGIN:VEVENT
SUMMARY:Moduli spaces of principal bundles on projective varieties
DTSTART;VALUE=DATE-TIME:20131010T103000Z
DTEND;VALUE=DATE-TIME:20131010T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3249@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
3249
LOCATION:Colaba Campus
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3249
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some Problems in Affine Algebraic Geometry
DTSTART;VALUE=DATE-TIME:20131031T103000Z
DTEND;VALUE=DATE-TIME:20131031T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3273@cern.ch
DESCRIPTION:ABSTRACT:\n\nIn this talk I will present a brief survey on a\n
few celebrated problems in affine algebraic geometry and their\ninterconne
ctions\, with special emphasis on the Cancellation Problem.\n\nhttps://ind
ico.tifr.res.in/indico/conferenceDisplay.py?confId=3273
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3273
END:VEVENT
BEGIN:VEVENT
SUMMARY:Morse theory on the space of paths in Homogeneous Space
DTSTART;VALUE=DATE-TIME:20131121T103000Z
DTEND;VALUE=DATE-TIME:20131121T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3301@cern.ch
DESCRIPTION:Homotopy connectedness theorems for complex submanifolds of\nf
lag manifolds G/P (referred to as theorems of Barth-Lefschetz type) have\n
been established by a number of authors. Morse Theory on the space of path
s leads to an elegant proof of homotopy connectedness theorems for\ncomple
x submanifolds of Hermitian symmetric spaces. In this talk we\nsketch how
to extend this proof to a larger class of flag manifolds\nwhich include G/
B where G is simple and B is a Borel subgroup.\n\nhttps://indico.tifr.res.
in/indico/conferenceDisplay.py?confId=3301
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3301
END:VEVENT
BEGIN:VEVENT
SUMMARY:On a Result of Moeglin and Waldspurger in Residual Characteristic
2
DTSTART;VALUE=DATE-TIME:20131128T103000Z
DTEND;VALUE=DATE-TIME:20131128T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3317@cern.ch
DESCRIPTION:ABSTRACT:\n\nLet $F$ be a finite extension of $\\QQ_p$\, ${\\b
f G}$ a connected\nreductive group over $F$\, and $\\pi$ an irreducible ad
missible representation\nof ${\\bf G}(F)$. A result of C. Moeglin and J.-L
. Waldspurger\nstates that\, if the residual characteristic of $F$ is diff
erent from $2$\,\nthen the `leading' coefficients in the character expansi
on of $\\pi$ at the\nidentity element of ${\\bf G}(F)$ give the dimensions
of certain spaces of\ndegenerate Whittaker forms.\n\nWe discuss how to ex
tend their result to residual characteristic $2$.\nThe outline of the proo
f is the same as in the original paper\nof Moeglin and Waldspurger\, but\n
certain constructions need to be modified to accommodate the case\nof even
residual characteristic.\n\nhttps://indico.tifr.res.in/indico/conferenceD
isplay.py?confId=3317
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3317
END:VEVENT
BEGIN:VEVENT
SUMMARY:On a conjecture of Colliot-Th'el`ene concerning quadratic spaces
DTSTART;VALUE=DATE-TIME:20131205T103000Z
DTEND;VALUE=DATE-TIME:20131205T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3324@cern.ch
DESCRIPTION:ABSTRACT:\n\nLet $X$ be an affine smooth complex algebraic var
iety and let $(V\,q)$\nbe a quadratic space over the ring of regular funct
ion on $X$. Let $u$ be an invirtible regular function on $X$. Assume that
$q$ represents $u$ over\nthe rational functions on $X$. We will prove that
for any point $x$ in $X$\nthe space $q$ represents the function $u$ in th
e local ring $O_{X\,x}$ of\nthe point $x$. This solves in affirmative the
conjecture of\nColliot-Th'el`ene mentioned in the title.\n\nhttps://indico
.tifr.res.in/indico/conferenceDisplay.py?confId=3324
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3324
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modular forms and $p$-adic representations
DTSTART;VALUE=DATE-TIME:20131219T103000Z
DTEND;VALUE=DATE-TIME:20131219T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3349@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
3349
LOCATION:Colaba Campus Lecture Room AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3349
END:VEVENT
BEGIN:VEVENT
SUMMARY:No Title
DTSTART;VALUE=DATE-TIME:20131226T103000Z
DTEND;VALUE=DATE-TIME:20131226T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3362@cern.ch
DESCRIPTION:This talk is based in part on a joint work with D. Vogan. The
set of \ninvolutions in a Weyl group (for example the symmetric group) can
be viewed as a basis of a vector space on which the Weyl group acts. This
representation of the Weyl group can be deformed to a q-analogue which is
a representation of the Hecke algebra. From this representation one can e
xtract some new polynomials indexed by a pair of involutions which general
ize the polynomials introduced in 1979 in my paper with Kazhdan.\n\nhttps:
//indico.tifr.res.in/indico/conferenceDisplay.py?confId=3362
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3362
END:VEVENT
BEGIN:VEVENT
SUMMARY:The pro-p-Iwahori Hecke algebra
DTSTART;VALUE=DATE-TIME:20140102T103000Z
DTEND;VALUE=DATE-TIME:20140102T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3376@cern.ch
DESCRIPTION:ABSTRACT:\n\nThe pro-p-Iwahori Hecke algebra H of a reductive
p-adic group G over a\ncommutative ring R is a deformation of the R-alge
bra of a variant of an\naffine Weyl group. When R is a field of characteri
stic p\, it is an\nimportant tool to study the R-representations of G\,
and deep relations\nbetween the H-modules and the representations of loca
l Galois groups have\nbeen discovered. We will describe the Ram-Goertze al
cove walks bases of H\nand the Bernstein relations\, essential to understa
nd the structure of H \nand its modules.\n\nhttps://indico.tifr.res.in/in
dico/conferenceDisplay.py?confId=3376
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3376
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cohomology of the moduli space of curves
DTSTART;VALUE=DATE-TIME:20140211T060000Z
DTEND;VALUE=DATE-TIME:20140211T070000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3464@cern.ch
DESCRIPTION:ABSTRACT:\n\nThe moduli space of curves carries tautological c
ohomology\nclasses. I will discuss the study of relations amongst these cl
asses\nstarting with ideas of Mumford in 1980s. The subject advanced in th
e 1990s\nwith conjectures of Faber and Faber-Zagier. I will explain the cu
rrent state of affairs based on Pixton's conjectures related to cohomologi
cal field theories. The talk represents joint work with A. Pixton and D. Z
vonkine.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
3464
LOCATION:Colaba Campus
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3464
END:VEVENT
BEGIN:VEVENT
SUMMARY:Triple Intersection Formulas for Isotropic Grassmannians
DTSTART;VALUE=DATE-TIME:20140213T103000Z
DTEND;VALUE=DATE-TIME:20140213T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3463@cern.ch
DESCRIPTION:ABSTRACT:\nA K-theoretic Pieri formula provides a convenient w
ay to calculate the\nproduct of arbitrary Schubert classes with certain sp
ecial classes in the\nGrothendieck ring of a homogeneous space. In this t
alk we calculate the\nK-theoretic triple intersection numbers of Pieri typ
e\, for Grassmannians of\ntypes B\, C\, and D. These can be used to quick
ly compute K-theoretic Pieri\ncoefficients\, which are alternating sums of
triple intersection numbers.\n\nOur method generalizes a geometric argume
nt used by Hodge to prove the\nclassical Pieri rule\, and requires us to e
xamine the projected Richardson\nvarieties in the underlying projective sp
ace of the Grassmannian. The\nequations defining these projected Richards
on varieties have applications\noutside of K-theory as well. Time permitt
ing\, we will discuss their use in\nstudying the equivariant cohomology of
Grassmannians of types B\, C\, and D.\n\nhttps://indico.tifr.res.in/indic
o/conferenceDisplay.py?confId=3463
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3463
END:VEVENT
BEGIN:VEVENT
SUMMARY:On rigidity theory for nonlinear interval exchange transformations
DTSTART;VALUE=DATE-TIME:20140218T090000Z
DTEND;VALUE=DATE-TIME:20140218T100000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3473@cern.ch
DESCRIPTION:In this talk we shall report on recent progress in rigidity th
eory for \nnonlinear interval exchange transformations corresponding \nto
cyclic permutations. Such maps can be viewed as circle homeomorphisms\nwit
h multiple break points. We shall discuss both recent results on \nrigidit
y and renormalization of such maps in case of one break point \n(joint wit
h S. Kocic and A. Teplinsky)\, and an extension to the \nmultiple-break se
tting (based on work in progress with A. Teplinsky).\n\nhttps://indico.tif
r.res.in/indico/conferenceDisplay.py?confId=3473
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3473
END:VEVENT
BEGIN:VEVENT
SUMMARY:Galois Representations
DTSTART;VALUE=DATE-TIME:20140227T103000Z
DTEND;VALUE=DATE-TIME:20140227T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3495@cern.ch
DESCRIPTION:In the last 30 years representations of (infinite) Galois grou
ps have played an increasingly important role in number theory. Indeed\, a
rithmetic objects such as the Diophantine equation $y=x^3-x^2+1$ or $x^n+y
^n=z^n$ often have attached Galois representations that `know' the solutio
ns. This talk will survey a small slice of this theory and will be\nacces
sible to mathematicians in all disciplines.\n\nhttps://indico.tifr.res.in/
indico/conferenceDisplay.py?confId=3495
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3495
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Gauss-Bonnet formula for moduli spaces of Riemann surfaces
DTSTART;VALUE=DATE-TIME:20140320T103000Z
DTEND;VALUE=DATE-TIME:20140320T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3532@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
3532
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3532
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Embedding theorems on hyperelliptic varieties'.
DTSTART;VALUE=DATE-TIME:20140410T103000Z
DTEND;VALUE=DATE-TIME:20140410T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3584@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
3584
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3584
END:VEVENT
BEGIN:VEVENT
SUMMARY: Tian-Todorov theorem for varieties with potentials
DTSTART;VALUE=DATE-TIME:20140514T103000Z
DTEND;VALUE=DATE-TIME:20140514T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3677@cern.ch
DESCRIPTION:I will report on a recent joint work with L. Katzarkov and\nM.
Kontsevich on the deformation theory of varieties equipped with\nholomorp
hic functions. I will discuss various generalizations of the\nunobstructed
ness\ntheorem for deformations of compact Calabi-Yau manifolds. In\npartic
ular I will explain a Tian-Todorov theorem for the deformations\nof Land
au-Ginzburg models and will explain the new Hodge theoretic\nstatements ne
eded in the proof. I will also discuss the various\ndefinitions of Hodge n
umbers for non-commutative\nHodge structures of Landau-Ginzburg type and t
he role they play in\nmirror symmetry.\n\nhttps://indico.tifr.res.in/indic
o/conferenceDisplay.py?confId=3677
LOCATION:Colaba Campus AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3677
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Constructions in shifted symplectic geometry'
DTSTART;VALUE=DATE-TIME:20140515T103000Z
DTEND;VALUE=DATE-TIME:20140515T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3675@cern.ch
DESCRIPTION:I will introduce a version of algebraic symplectic geometry\nt
hat is suitable for dealing with singular or stacky spaces. I will\nexplai
n how this generalization arises naturally in the study of\nmoduli spaces
and will outline the connections to ordinary symplectic\ngeometry. I will
also give interesting examples and will describe a\nseveral non-trivial co
nstructions of shifted symplectic structures.\nThis is a joint work with T
oen\, Vaquie\, and Vezzosi.\n\n\nhttps://indico.tifr.res.in/indico/confere
nceDisplay.py?confId=3675
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3675
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euclidean Geometry\, Analysis and Physics (Aset Colloquium)
DTSTART;VALUE=DATE-TIME:20140725T103000Z
DTEND;VALUE=DATE-TIME:20140725T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3789@cern.ch
DESCRIPTION:Pythagoras and Euclid had limited tools\, but unlimited curios
ity. Understanding interesting geometric objects and phenomena beyond tria
ngles and circles and their intersections needs more sophisticated tools (
technology) from algebra and analysis. These tools were developed only in
the last three hundred years. Modern functional\nanalysis\, Lie groups and
representation theory may be seen as natural continuations of what Pythag
oras and Euclid started.\nSome of the most interesting features of the pro
gress of Euclidean geometry were repeated at an accelerated rate in the de
velopment of special relativity and relativistic quantum theory\, almost a
s if ``ontogeny recapitulates phylogeny" in the words of biologists. What
took more than two thousand years in the history of Euclidean geometry was
in some sense repeated in modern physics just in the span of about 50 yea
rs!\n\nThis talk will give an overview of this surprising history ranging
from Pythagoras (500 BC) to Wigner (1940)\, and a popular account of the n
ew tools from algebra and analysis which made the modern progress possible
.\n\nDisclaimer: The speaker is not a historian\, and some of the above st
ory involves a fanciful reconstruction of history. However\, he promise to
try his best that at least the mathematics will be correct.\n\nhttps://in
dico.tifr.res.in/indico/conferenceDisplay.py?confId=3789
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3789
END:VEVENT
BEGIN:VEVENT
SUMMARY:Period-index bounds for the Brauer group
DTSTART;VALUE=DATE-TIME:20140808T103000Z
DTEND;VALUE=DATE-TIME:20140808T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3820@cern.ch
DESCRIPTION:Over number fields\, period and index of elements in the Braue
r\ngroup coincide. Bounds for the index in terms of the period has conse
quences for quadratic forms. We shall explain how period index bounds lead
to bounding the anisotropic dimension of quadratic forms over certain cla
sses of function fields.\n\nhttps://indico.tifr.res.in/indico/conferenceDi
splay.py?confId=3820
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3820
END:VEVENT
BEGIN:VEVENT
SUMMARY:Intersection Theorems for Finite Sets
DTSTART;VALUE=DATE-TIME:20140811T103000Z
DTEND;VALUE=DATE-TIME:20140811T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3831@cern.ch
DESCRIPTION:Finite extremal set theory is concerned with the following gen
eral problem:\nSuppose we have a collection $F$ of subsets of an $n$-eleme
nt set and we\nhave some restriction on the possible intersection sizes of
pairs of sets in\n$F$. What is the maximum number of subsets that $F$ can
contain?\nSurprisingly\, solutions to various special cases of this probl
em have deep\nimplications in many other areas\, including coding theory\,
geometry\, and\ncomputer science. A particular famous example is due to F
rankl and Rodl\, who\nsolved a 250-dollar problem of Erdos by proving that
if $n$ is a multiple of\n4\nand $n/4$ is excluded as an intersection size
\, then $|F|<(1.99)^n$. We\nextend this result by showing that if some add
itional (rather mild)\nrestrictions are placed on the possible intersectio
n sizes\, then $|F|<\n(1.63)^n$. The talk is intended for a general mathem
atical audience. This is\njoint work with Vojtech Rodl.\n\nhttps://indico.
tifr.res.in/indico/conferenceDisplay.py?confId=3831
LOCATION:Colaba Campus AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3831
END:VEVENT
BEGIN:VEVENT
SUMMARY:Effective Ratner equidistribution result for $\\mathrm{SL}(2\, \\m
athbb R)\\ltimes \\mathbb R^{2k} $ and applications to quadratic forms.
DTSTART;VALUE=DATE-TIME:20140814T103000Z
DTEND;VALUE=DATE-TIME:20140814T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3832@cern.ch
DESCRIPTION:Let $G=\\mathrm{SL}(2\,\\mathbb R)\\ltimes \\mathbb R^{2k}$ an
d let $\\Gamma$\nbe a congruence subgroup of $\\mathrm{SL}(2\,\\mathbb Z)\
\ltimes\\mathbb Z^{2k}$.\nWe give an effective equidistribution result for
a family of 1-dimensional\nunipotent orbits in $\\Gamma\\backslash G$. Th
e proof involves Specral methods\nand bounds for exponential sums. We appl
y this result to obtain an effective\nOppenheim type result for a class of
indefinate irrational quadratic forms.\nThis is based on a joint work wit
h Andreas Strombergsson.\n\nhttps://indico.tifr.res.in/indico/conferenceDi
splay.py?confId=3832
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3832
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Deligne-Kazhdan theory and its applications to the local Lang
lands correspondence.
DTSTART;VALUE=DATE-TIME:20140904T103000Z
DTEND;VALUE=DATE-TIME:20140904T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3874@cern.ch
DESCRIPTION:The ``complex'' representation theory of Galois groups and spl
it reductive groups over a local field of characteristic p can be viewed a
s the ``limit'' of the representation theory of these groups over local fi
elds of characteristic 0 with the same residue field\, as the ramification
index tends to infinity.\n\nIn this talk\, we will begin by briefly revie
wing this theory. We will see\nhow this technique\, combined with the work
of Gan-Takeda on the local Langlands correspondence (LLC) for GSp(4\,F) f
or local fields F of characteristic 0\, can be used to prove the LLC for G
Sp(4\,F') for a local function field F' of odd characteristic.\n\nhttps://
indico.tifr.res.in/indico/conferenceDisplay.py?confId=3874
LOCATION:Colaba Campus AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3874
END:VEVENT
BEGIN:VEVENT
SUMMARY:Equivalence relations on algebraic cobordism
DTSTART;VALUE=DATE-TIME:20141009T103000Z
DTEND;VALUE=DATE-TIME:20141009T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3927@cern.ch
DESCRIPTION:Algebraic cobordism gives a lifting of the topological theory
of\ncomplex cobordism to the setting of algebraic geometry. As in the case
of complex cobordism\, algebraic cobordism is closely related to formal g
roup laws\, which allows one to construct many new theories from algebraic
cobordism. In particular\, algebraic $K$-theory and the Chow ring can be
obtained in this way. It is an interesting question to ask whether various
adequate equivalences for algebraic cycles can be lifted up to the level
of algebraic cobordism cycles. After briefly introducing the definition
and construction of algebraic cobordism\, I will talk about analogues of w
ell-studied equivalence relations at the level of algebraic cobordism cycl
es and compare them with each other. In particular\, I will discuss the be
haviour of algebraic cobordism modulo numerical equivalence as a cohomolog
y theory. This work is done jointly with Jinhyun Park.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=3927
LOCATION:Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3927
END:VEVENT
BEGIN:VEVENT
SUMMARY: An algebraic proof of the Involutivity theorem
DTSTART;VALUE=DATE-TIME:20141016T103000Z
DTEND;VALUE=DATE-TIME:20141016T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-3947@cern.ch
DESCRIPTION:An important geometric invariant in the theory of $D$-modules
is the\ncharacteristic variety and its intvolutivity is a vital result in
this\ntheory. In this talk\, we discuss an algebraic proof of the involuti
vity\ntheorem which says that the characteristic ideal of a module is cl
osed\nunder a Poisson bracket.\n\nhttps://indico.tifr.res.in/indico/confer
enceDisplay.py?confId=3947
LOCATION:Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=3947
END:VEVENT
BEGIN:VEVENT
SUMMARY:Configurations in lattices
DTSTART;VALUE=DATE-TIME:20141113T103000Z
DTEND;VALUE=DATE-TIME:20141113T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4007@cern.ch
DESCRIPTION:We discuss the problem whether one can find approximate\nn-poi
nt configurations in lattices in the Euclidean space and\nmore generally i
n lattice in other groups. It turns out that this\nproblem is closely rela
ted to the limiting behaviour of higher-order correlations. This is joint
work with M. Einsiedler\nand M. Bjoerklund.\n\nhttps://indico.tifr.res.in/
indico/conferenceDisplay.py?confId=4007
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4007
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some recent results on Diophantine equations: a survey
DTSTART;VALUE=DATE-TIME:20141127T103000Z
DTEND;VALUE=DATE-TIME:20141127T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4035@cern.ch
DESCRIPTION:The study of Diophantine equations is among the oldest topics\
ninvestigated by mathematicians. It is known that some problems will never
be solved\, yet fundamental progress has been achieved recently.\nWe surv
ey some of the main results and some of the main conjectures.\n\nhttps://i
ndico.tifr.res.in/indico/conferenceDisplay.py?confId=4035
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4035
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iwasawa theory and Chern Classes
DTSTART;VALUE=DATE-TIME:20141204T103000Z
DTEND;VALUE=DATE-TIME:20141204T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4060@cern.ch
DESCRIPTION:The first Chern class has something to do with the main conjec
ture\nof Iwasawa theory. I will make this statement precise in both the\nc
ommutative and non-commutative setting. Then I will raise some questions a
bout the possible role of higher Chern classes in Iwasawa theory and prese
nt a modest development towards providing answers to some of the questions
. (This is a work in progress jointly with F. Bleher\, T. Chinburg\, R. Gr
eenberg\, G. Pappas\, R. Sharifi and M. Taylor).\n\nhttps://indico.tifr.re
s.in/indico/conferenceDisplay.py?confId=4060
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4060
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non-arithmetic lattices
DTSTART;VALUE=DATE-TIME:20141208T103000Z
DTEND;VALUE=DATE-TIME:20141208T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4067@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
4067
LOCATION: AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4067
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solving $S$-unit and Mordell equations via Shimura-Taniyama conje
cture.
DTSTART;VALUE=DATE-TIME:20141211T103000Z
DTEND;VALUE=DATE-TIME:20141211T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4081@cern.ch
DESCRIPTION:We present two types of algorithms that practically solve S-un
it and\nMordell equations. The first type builds on Cremona's algorithm\,
and\nthe second one combines explicit height bounds with enumeration\nalgo
rithms. In particular we refine de Weger's sieve for S-unit\nequations and
solve a large class of such. Additionally our new\nresults on Mordell's e
quation implies an improved version of a theorem\nof Coates on the differe
nce of coprime squares and cubes. Our results and algorithms crucially rel
y on a method of Faltings (Arakelov\, Parsin\, Szpiro) combined with the S
himura-Taniyama conjecture\, and they do not use the theory of logarithmic
forms.\nThis is joint work with Rafael von Känel.\n\nhttps://indico.tifr
.res.in/indico/conferenceDisplay.py?confId=4081
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4081
END:VEVENT
BEGIN:VEVENT
SUMMARY:Why the foundation of differential topology is deeply related to t
he foundation of quatum field theory
DTSTART;VALUE=DATE-TIME:20141218T103000Z
DTEND;VALUE=DATE-TIME:20141218T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4092@cern.ch
DESCRIPTION:How we perturb the diagonal $M \\subset M\\times M$\nis known
to be related to the foundation of differential\ntopology. The same point
is related to the problem of inifinity in??\nquatum field theory.\n\nI wan
t to explain how they are related to each other and also to\nfoundation of
the theory of pseudo-holomorphic curve\ntopological field theory or renom
alization.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confI
d=4092
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4092
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conjectures on non-vanishing of quadratic twists of $L$-functions
modulo a prime.
DTSTART;VALUE=DATE-TIME:20150115T103000Z
DTEND;VALUE=DATE-TIME:20150115T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4139@cern.ch
DESCRIPTION:This will be a description of precise conjectures (due mostly
to K.\nPrasanna) about the $p$-adic valuation of quadratic twisted $L$-fun
ctions at the centre of the critical strip\, and an approach we propose to
prove them\, based on work of Wei Zhang.\n\nhttps://indico.tifr.res.in/in
dico/conferenceDisplay.py?confId=4139
LOCATION: AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4139
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modular TQFT-representations of mapping class groups.
DTSTART;VALUE=DATE-TIME:20150122T103000Z
DTEND;VALUE=DATE-TIME:20150122T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4140@cern.ch
DESCRIPTION:There are by now several mathematical constructions of\nTopolo
gical Quantum Field Theories (TQFT) as defined by Atiyah and\nSegal. These
TQFTs give rise to finite-dimensional complex unitary\nrepresentations of
mapping class groups of surfaces. I will explain\nthat in some cases\,
one can also get modular representations (i.e.\,\nrepresentations in finit
e characteristic)\, using some integrality\nproperties of the TQFT. As a
n application\, I will discuss joint work\nwith Reid where we use these re
presentations to answer a question\nof Hamenstaedt about finite index subg
roups of the mapping class\ngroup. I will also present Verlinde-like dimen
sion formulas for the\nirreducible factors of these representations in the
case of equal\ncharacteristic.\n\nhttps://indico.tifr.res.in/indico/confe
renceDisplay.py?confId=4140
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4140
END:VEVENT
BEGIN:VEVENT
SUMMARY:Foliated topology and foliated homotopy types
DTSTART;VALUE=DATE-TIME:20150129T103000Z
DTEND;VALUE=DATE-TIME:20150129T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4170@cern.ch
DESCRIPTION:In this talk I will motivate the introduction of a new Grothen
dieck topology on algebraic varieties (and more precisely on foliated sche
mes). Then\, I'll describe a recipe for computing the foliated cohomology
at the generic point of an algebraic variety.\n\nhttps://indico.tifr.res.i
n/indico/conferenceDisplay.py?confId=4170
LOCATION:Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4170
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enumerative geometry of singular curves in a general linear system
.
DTSTART;VALUE=DATE-TIME:20150305T103000Z
DTEND;VALUE=DATE-TIME:20150305T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4249@cern.ch
DESCRIPTION:Enumerative geometry of singular plane curves (i.e. curves i
n\n$CP^2$)\nis a classical subject dating back to nineteenth century. A mo
re\ngeneral\nclass of question is to consider a general linear system $L--
->X$\nover a compact complex manifold and enumerate singular curves in\n
this linear system. In this talk we will describe a topologcial\nmethod
to approach questions of this nature. The basic idea is to\nexpress these
enumerative numbers as the Euler class of some\nappropriate bundle. If t
ime permits\, we will give a brief idea\nabout how to compute degenerate c
ontributions to the Euler class\nusing topological methods.\n\nhttps://ind
ico.tifr.res.in/indico/conferenceDisplay.py?confId=4249
LOCATION:Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4249
END:VEVENT
BEGIN:VEVENT
SUMMARY: Enumerative geometry of singular curves in a general linear syste
m.
DTSTART;VALUE=DATE-TIME:20150305T103000Z
DTEND;VALUE=DATE-TIME:20150305T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4259@cern.ch
DESCRIPTION:Enumerative geometry of singular plane curves (i.e. curves i
n $CP^2$) is a classical subject dating back to nineteenth century. A more
general class of question is to consider a general linear system $L--->X$
over a compact complex manifold and enumerate singular curves in this l
inear system. In this talk we will describe a topologcial method to ap
proach questions of this nature. The basic idea is to express these enumer
ative numbers as the Euler class of some appropriate bundle. If time per
mits\, we will give a brief idea about how to compute degenerate contribut
ions to the Euler class using topological methods.\n\nhttps://indico.tifr.
res.in/indico/conferenceDisplay.py?confId=4259
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4259
END:VEVENT
BEGIN:VEVENT
SUMMARY:Normality and $K_1$-stability of Roy's elementary orthogonal group
DTSTART;VALUE=DATE-TIME:20150312T103000Z
DTEND;VALUE=DATE-TIME:20150312T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4260@cern.ch
DESCRIPTION:ABSTRACT:\n\nA. Roy introduced the elementary orthogonal group
$\\EO_A(Q\\perp H(A)^m)$\nof a quadratic space with a hyperbolic summand
over a commutative ring \n$A$. This construction of Roy generalized the ea
rlier work's of\nDickson-Siegel-Eichler-Dieudonn\\'{e} over fields.\n\nIn
this talk\, we shall discuss the normality of the elementary orthogonal\ng
roup (Dickson--Siegel--Eichler--Roy or DSER group) $\\EO_A(Q\\perp H(A)^m)
$\nunder some conditions on the hyperbolic rank. We also establish stabil
ity\nresults for $K_1$ of Roy's elementary orthogonal group under differe
nt\nstable range conditions. The stability problem for $K_1$ of quadratic\
nforms was studied in 1960's and in early 1970's by H. Bass\, A. Bak\, A.\
nRoy\, M. Kolster and L.N. Vaserstein. We obtain a Dennis-Vaserstein type\
ndecomposition theorem for the elementary orthogonal group (DSER group)\nw
hich is used to deduce the stability theorem.\n\nhttps://indico.tifr.res.i
n/indico/conferenceDisplay.py?confId=4260
LOCATION:Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4260
END:VEVENT
BEGIN:VEVENT
SUMMARY:An introduction to the geometric Satake isomorphism
DTSTART;VALUE=DATE-TIME:20150330T103000Z
DTEND;VALUE=DATE-TIME:20150330T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4293@cern.ch
DESCRIPTION:The Satake isomorphism\, which describes the spherical Hecke\n
algebra of a p-adic group in terms of the representation ring of its\nLang
lands dual group\, is the starting point of the Langlands duality. \nI wil
l give an introduction to its categorical version\, known as the geometric
Satake correspondence. Time permitting\, I will also discuss its\napplica
tions.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=42
93
LOCATION:TIFR\, Mumbai AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4293
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quasicrystals and Diophantine approximation
DTSTART;VALUE=DATE-TIME:20150521T103000Z
DTEND;VALUE=DATE-TIME:20150521T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4375@cern.ch
DESCRIPTION:In this talk we will begin with a brief history of the\nmathem
atics of aperiodic tilings of Euclidean space\, highlighting the\nrelevanc
e to the theory of quasicrystals. Next we will focus on an\nimportant coll
ection of point sets\, cut and project sets\, which come from a\ndynamical
construction and provide us with a mathematical model for\nquasicrystals.
After giving definitions and examples of these sets\, we will\ndiscuss th
eir relationship with Diophantine approximation\, and show how the\ninterp
lay between these two subjects has recently led to new results in\nboth of
them.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=43
75
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4375
END:VEVENT
BEGIN:VEVENT
SUMMARY:HyperKahler manifolds and Seiberg-Witten equations
DTSTART;VALUE=DATE-TIME:20150604T103000Z
DTEND;VALUE=DATE-TIME:20150604T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4385@cern.ch
DESCRIPTION:In this talk\, I will discuss the so called nonlinear gauged\n
sigma model in dimension four. An important element of the construction is
\na nonlinear generalization of the Dirac operator on a 4-manifold such th
at\nthe fiber of the spinor vector bundle\, a copy of quaternions H\, is r
eplaced\nby a hyperKahler manifold admitting certain symmetries. This Dira
c operator\nis used to define a generalization of the Seiberg-Witten equat
ions.\nHowever\, the candidate hyperKahler manifolds are neither compact n
or\ncomplete and therefore the compactification of the moduli space of\nso
lutions poses a challenge. I will discuss some progress made in this\ndire
ction. I will also describe a ``dimensional reduction" of the above\ntheor
y to two-dimensions which produce a Higgs-field and the equations we\nobta
in generalize the Symplectic Vortex equations.\n\nhttps://indico.tifr.res.
in/indico/conferenceDisplay.py?confId=4385
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4385
END:VEVENT
BEGIN:VEVENT
SUMMARY:A degeneration of moduli of Hitchin pairs
DTSTART;VALUE=DATE-TIME:20150626T103000Z
DTEND;VALUE=DATE-TIME:20150626T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4422@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
4422
LOCATION:TIFR\, Mumbai AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4422
END:VEVENT
BEGIN:VEVENT
SUMMARY:A degeneration of moduli of Hitchin pairs
DTSTART;VALUE=DATE-TIME:20150626T103000Z
DTEND;VALUE=DATE-TIME:20150626T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4423@cern.ch
DESCRIPTION:In this talk\, I will discuss the construction and study a deg
eneration of the\nmoduli space\nof Higgs bundles of rank n and degree d\;
this degeneration has analytic normal\ncrossing singularities. \nCentral t
o this theory is the geometry of the Hitchin fibre which reveals asomewhat
\nnew aspect of the theory of compactifications of Picard varieties of\ncu
rves\, which at the same time yields a degeneration of the classical Hitch
in\npicture. In contrast to the usual theory of Picard compactifications\,
the ones\nwhich arise here have analytic normal crossing singularities. A
natural toric\npicture shows\nup\, which in a certain sense underlies the
so-called abelianization philosophy.\n\nIt is based on joint work with P.
Barik and D.S. Nagaraj.\n\nhttps://indico.tifr.res.in/indico/conferenceDi
splay.py?confId=4423
LOCATION: AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4423
END:VEVENT
BEGIN:VEVENT
SUMMARY:Big image of Galois for positive slope families
DTSTART;VALUE=DATE-TIME:20150709T103000Z
DTEND;VALUE=DATE-TIME:20150709T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4430@cern.ch
DESCRIPTION:In the 90's\, Coleman and Mazur defined the Eigencurve\n$X$ wh
ich parametrizes the Hecke eigensystems of modular forms \nwith non zero e
igenvalue for $U_p$. Recently\, Hida showed that non CM\nordinary families
have big Galois image. We do the same\, in the non ordinary case\, for fa
milies of finite slope on $X$. The ingredient replacing ordinarity is Sen'
s theory in the relative setting.\n\nhttps://indico.tifr.res.in/indico/con
ferenceDisplay.py?confId=4430
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4430
END:VEVENT
BEGIN:VEVENT
SUMMARY:On bases for local Weyl modules in type A
DTSTART;VALUE=DATE-TIME:20150910T103000Z
DTEND;VALUE=DATE-TIME:20150910T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4554@cern.ch
DESCRIPTION:Let \\gg be a complex simple Lie algebra and \\gg[t]=\\gg \\ot
imes \\CC[t]\nthe corresponding current algebra. Local Weyl modules\, intr
oduced by Chari\nand Pressley\, are interesting finite-dimensional \\gg[t]
-modules.\nChari-Pressley also produced nice monomial bases for these modu
les in the\ncase \\gg=sl_2. Later\, Chari and Loktev clarified and extende
d the\nconstruction of these bases to the case \\gg=sl_m. In joint work wi
th K.\nN. Raghavan and S. Viswanath\, we study stability of these bases f
or\nnatural inclusions of local Weyl modules. We also introduce the notio
n of\n"partition overlay pattern" (POP) to reinterpret the indexing set of
\nthese bases. The notion of a POP leads naturally to the notion of the\n"
area" of a Gelfand-Tsetlin pattern\, and we prove that there exists a\nun
ique Gelfand-Tsetlin pattern of maximum area among all those with fixed\nb
ounding sequence and weight.\n\nhttps://indico.tifr.res.in/indico/conferen
ceDisplay.py?confId=4554
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4554
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Holomorphic Cartan geometry'
DTSTART;VALUE=DATE-TIME:20160407T103000Z
DTEND;VALUE=DATE-TIME:20160407T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-4946@cern.ch
DESCRIPTION:Recalling the defintion of holomorphic Cartan geometries\nsome
of their properties will be explained.\n\nhttps://indico.tifr.res.in/indi
co/conferenceDisplay.py?confId=4946
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=4946
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Values of quadratic forms'
DTSTART;VALUE=DATE-TIME:20170612T103000Z
DTEND;VALUE=DATE-TIME:20170612T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5700@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
5700
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5700
END:VEVENT
BEGIN:VEVENT
SUMMARY:The inverse and implicit function Theorems
DTSTART;VALUE=DATE-TIME:20170615T103000Z
DTEND;VALUE=DATE-TIME:20170615T120000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5706@cern.ch
DESCRIPTION:The inverse and implicit function theorems for smooth function
s on open\nsets in Euclidean spaces \\R^n are the foundations on which dif
ferential\ntopology is built. The real analytic versions of the theorems h
ave\nanalogues over p-adic fields as well. In this talk I will give a proo
f\nof analytic version of the theorems which works uniformly for the p-adi
c\ncases as well as the real or complex cases. I will also indicate some\n
interesting applications of the theorems\n\nhttps://indico.tifr.res.in/ind
ico/conferenceDisplay.py?confId=5706
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5706
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jordan Curve theorem
DTSTART;VALUE=DATE-TIME:20170622T103000Z
DTEND;VALUE=DATE-TIME:20170622T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5718@cern.ch
DESCRIPTION:A proof of this theorem will be given under some extra assumpt
ions. And if\ntime permits\, some discussion of how this theorem generalis
es to higher\ndimension.\n\nhttps://indico.tifr.res.in/indico/conferenceDi
splay.py?confId=5718
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5718
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representation stability and FI-modules
DTSTART;VALUE=DATE-TIME:20170706T103000Z
DTEND;VALUE=DATE-TIME:20170706T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5715@cern.ch
DESCRIPTION:We often encounter sequences of representations of a family of
groups. For example\, the cohomology of ordered configurations of n di
stinct points on a manifold is a representation of the symmetric group Sn
. Similarly\, the homology of the congruence subgroup of level m ins
ide GLn(Z) is a representation of GLn(Z/mZ). As n grows to infini
ty the two examples above become\, in a sense\, stable as representations.
Stable representations can be thought of as finitely generated objects in
a suitable functor category. This point of view is due to Church-Ellenber
g-Farb who introduced and studied such a category called FI-modules. We pr
ovide an introduction to FI-modules and explain what it entails about the
examples above.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?
confId=5715
LOCATION:TIFR A-369
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5715
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elliptic curves and the Birch and Swinnerton-Dyer conjecture
DTSTART;VALUE=DATE-TIME:20170713T023000Z
DTEND;VALUE=DATE-TIME:20170713T033000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5740@cern.ch
DESCRIPTION:Abstract:\nThe Birch and Swinnerton-Dyer conjecture\, one of t
he millenium problems\,\nis a bridge between algebraic invariants of an el
liptic curve and its\n(complex analytic) L-function. In the case of low ra
nks\, we prove this\nconjecture up to the finitely many bad primes and the
prime 2\, by proving\nthe Iwasawa main conjecture in full generality. The
ideas in the proof and\nformulation also lead us to new and mysterious ph
enomena. This talk\nassumes no specialized background in number theory.\n\
nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5740
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5740
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Small Eigenvalues of Riemannian surfaces'
DTSTART;VALUE=DATE-TIME:20170803T103000Z
DTEND;VALUE=DATE-TIME:20170803T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5782@cern.ch
DESCRIPTION:Abstract:\n\nAny eigenvalue of the Laplace operator\, acting o
n the function space of a hyperbolic surface $S$\, below $1/4$ is called a
{\\it small or exceptional} eigenvalue of $S$. \nHistorically\, Selberg
’s $1/4$-conjecture was a motivation for the study of these eigenvalues.
\nExistence of hyperbolic surfaces having small eigenvalues was first obt
ained by B. Randol (1974\, \\cite{Ra}). \nLater P. Buser found a simpler c
onstruction of such surfaces (1977\, \\cite{Bu}).\nHe also found initial b
ounds on the number of small eigenvalues of a given surface depending on
the topology of the surface (1977\, \\cite{Bu}). \n\nLater P. Schumtz (199
1\, \\cite{Sch}) sharpened the methods developed by Buser and from his bou
nds he (and later Buser also) conjectured that the number of these eigenva
lues of a closed hyperbolic surface is at most the Euler characteristic of
the surface. An extended version of this conjecture was proved by Otal an
d Rosas (2009\, \\cite{OR}). In their paper Otal-Rosas asked if their resu
lt can be extended to all smooth surfaces. In a series of three papers \\c
ite{BMM1}\, \\cite{BMM2} and \\cite{BMM3}\, joint with Werner Ballmann and
Henrik Matthiesen\, we have answered an extended version of this last que
stion in the affirmative. In this talk I shall present a short survey of t
hese developments and results.\n\n\\bibitem[BMM1]{BMM1} W. Ballmann\, H. M
atthiesen\, S. Mondal\, Small eigenvalues of closed surfaces.\n\\emph{J. D
ifferential Geom.} 103 (2016)\, no. 1\, 1–13\, MR3488128\, Zbl 1341.5306
6.\n\n\n\\bibitem[BMM2]{BMM2} W. Ballmann\, H. Matthiesen\, S. Mondal\, Sm
all eigenvalues of surfaces of finite\ntype. \\emph{Compositio Math.} 153
(2017)\, 1747–1768\, MR\, Zbl.\n\\bibitem[BMM3]{BMM3} W. Ballmann\, H. M
atthiesen\, S. Mondal\, On the analytic systole of Riemannian\nsurfaces of
finite type. (submitted).\n\n\\bibitem[Bu]{Bu} P. Buser\, Geometry and sp
ectra of compact Riemann surfaces. Reprint of the\n1992 edition. Modern Bi
rkhäuser Classics. Birkhäuser\, 2010. xvi+454 pp.\,\nMR2742784\, Zbl 123
9.32001.\n\n\n\\bibitem[OR]{OR}J.-P. Otal\, E. Rosas\, Pour toute surface
hyperbolique de genre g\, $\\lambda_{2g-2} > 1/4.$\n\\emph{Duke Math. J.}
150 (2009)\, no. 1\, 101–115\, MR2560109\, Zbl 1179.30041.\n\n\n\\bibite
m[Ra]{Ra} B. Randol Small eigenvalues of the Laplace operator on compact R
iemann\nsurfaces. \\emph{Bull. Amer. Math. Soc.} 80 (1974)\, 996–1000.\n
\n\\bibitem[Sch]{Sch} P. Schmutz\, Small eigenvalues on Riemann surfaces o
f genus 2. \\emph{Invent. Math.}\n106 (1991)\, no. 1\, 121–138\, MR11233
77\, Zbl 0764.53035.\n\nhttps://indico.tifr.res.in/indico/conferenceDispla
y.py?confId=5782
LOCATION:TIFR\,Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5782
END:VEVENT
BEGIN:VEVENT
SUMMARY:The free product structure of diffeomorphism groups
DTSTART;VALUE=DATE-TIME:20170810T103000Z
DTEND;VALUE=DATE-TIME:20170810T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5793@cern.ch
DESCRIPTION:Abstract:\nI will discuss some aspects of the algebraic struct
ure of finitely\ngenerated groups of diffeomorphisms of compact one-manifo
lds. In\narticular\, we show that if $G$ is not virtually metabelian then
(G \\times\nZ)*Z cannot act faithfully by C^2 diffeomorphisms on a compact
\none-manifold. Among the consequences of this result is a completion of t
he\nclassification of right-angled Artin groups which admit faithful\nC^{\
\infty} actions on the circle\, a program initiated together with H.\nBaik
and S. Kim. This represents joint work with S. Kim.\n\nhttps://indico.tif
r.res.in/indico/conferenceDisplay.py?confId=5793
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5793
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Transcendence of certain infinite series'
DTSTART;VALUE=DATE-TIME:20170817T103000Z
DTEND;VALUE=DATE-TIME:20170817T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5816@cern.ch
DESCRIPTION:Abstract:\n\nThe problem of studying transcendental nature of
infinite\nseries owes its origin to classical mathematics. Such problems a
re not\ndiscrete in nature and often have a rich transcendence theory behi
nd. In\nthe first half\, we shall discuss few such examples. Then we shall
report\non a joint work with M. Ram Murty\, where we study transcendental
nature of\ncertain infinite series\, in the realm of the theory of E-func
tions.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=58
16
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5816
END:VEVENT
BEGIN:VEVENT
SUMMARY:Central extensions and A^1-fundamental groups
DTSTART;VALUE=DATE-TIME:20170914T103000Z
DTEND;VALUE=DATE-TIME:20170914T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5867@cern.ch
DESCRIPTION:Abstract:\n\nClassical results of Matsumoto and Suslin describ
e the universal central extension of the group of rational points of a spl
it\, semisimple\, simply connected algebraic group. These results were la
ter extended by Brylinski and Deligne\, who determined the category of cen
tral extensions of a reductive group by the second K-theory sheaf K_2. We
will discuss how these classical results can be uniformly explained and g
eneralized using the so-called motivic or A^1-fundamental group of a reduc
tive algebraic group and describe some interesting consequences. The talk
is based on joint work in progress with Fabien Morel.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=5867
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5867
END:VEVENT
BEGIN:VEVENT
SUMMARY:From extremal metrics and gradient flows to categorical Kähler ge
ometry.
DTSTART;VALUE=DATE-TIME:20170928T103000Z
DTEND;VALUE=DATE-TIME:20170928T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5901@cern.ch
DESCRIPTION:Abstract:\nThis talk is based on joint work with Fabian Haiden
\, Ludmil Katzarkov\, and\nMaxim Kontsevich. I will describe our attempts
to formalize and understand\nthe mathematical structures underlying the ph
ysical notion of stability\nfor D-branes in string theory. Our work builds
upon Bridgeland’s notion of\nstability conditions on triangulated categ
ories\, and is inspired by ideas\nfrom symplectic geometry\, non-Archimede
an geometry\, dynamical systems\,\ngeometric invariant theory\, and the Do
naldson-Uhlenbeck-Yau\ncorrespondence.\n\nhttps://indico.tifr.res.in/indic
o/conferenceDisplay.py?confId=5901
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5901
END:VEVENT
BEGIN:VEVENT
SUMMARY:Generalized Jacobian Conjecture
DTSTART;VALUE=DATE-TIME:20171012T103000Z
DTEND;VALUE=DATE-TIME:20171012T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5949@cern.ch
DESCRIPTION:Abstract:\n\nM. Miyanishi generelized the usual Jacobian Conje
cture as follows.\n\nGeneralized Jacobian Conjecture.\nLet V be a normal a
ffine variety. Suppose f:V \\to V is an unramified\nmorphism. Then f is a
proper morphism.\n\nAfter discussing some earlier positive results and som
e counterexamples to\nGJC we will outline the proof of the following resul
t proved jointly with\nM. Miyanishi.\n\nTheorem. Let V be an irreducible n
ormal affine surface. Assume that V has\nat least one singular point which
is not a quotient singular point. Then\nany unramified self morphism is a
n\nisomorphism.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?
confId=5949
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5949
END:VEVENT
BEGIN:VEVENT
SUMMARY:Involutions on algebraic surfaces and algebraic cycles
DTSTART;VALUE=DATE-TIME:20171109T103000Z
DTEND;VALUE=DATE-TIME:20171109T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-5996@cern.ch
DESCRIPTION:Abstract:\nConsider a smooth\, projective\, algebraic surface
S defined over\nthe field of complex numbers. Suppose that the surface is
equipped with an\ninvolution (an automorphism of order 2). Then the genera
lised Bloch\nconjecture predicts that\, if the involution acts identically
at the level\nof cohomology then it must act identically on the Chow grou
p of zero\ncycles of the surface.\n\nIn this talk we will survey some rece
nt progress in this direction and\ndiscuss the proof of the conjecture for
some special class of surfaces of\ngeneral type with geometric genus zero
.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5996
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=5996
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Prasad conjecture for PGSp(4)
DTSTART;VALUE=DATE-TIME:20171116T103000Z
DTEND;VALUE=DATE-TIME:20171116T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6011@cern.ch
DESCRIPTION:Abstract:\nPeriod Problem is one of the most popular interesti
ng problems\nin recently years\, such as the Gan-Gross-Prasad conjectures.
In this talk\,\nwe mainly focus on the local period problems\, so called
the relative local\nLanglands programs. Given a quadratic local field exte
nsion $E/F$ and a\nquasi-split reductive group $G$ defined over $F$ with a
ssociated quadratic\ncharacter $\\chi_G$\, let $\\pi$ be a smooth represen
tation of $G(E)$. Assume\nthe\nLanglands-Vogan conjecture\, Prof. Prasad g
ives a precise description for\nthe dimension $\\dim \\Hom_{G(F)}(\\pi\,\\
chi_G)$. We verify this conjecture if\n$\\pi$ is a discrete series represe
ntation and G=PGSp(4).\n\nhttps://indico.tifr.res.in/indico/conferenceDisp
lay.py?confId=6011
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6011
END:VEVENT
BEGIN:VEVENT
SUMMARY:The representability of motivic cohomology
DTSTART;VALUE=DATE-TIME:20171123T103000Z
DTEND;VALUE=DATE-TIME:20171123T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6027@cern.ch
DESCRIPTION:Abstract:\n\nAny algebraic variety $X$ over an algebraically c
losed field $k$ is\nassociated with its Albanese variety $Alb_X.$ Accordin
g to Rojtman\, for\nsmooth proper $X\,$ the torsion part of the group of r
ational points\n$Alb_X(k)$ is canonically isomorphic to $CH_0(X)_{tor}^0\,
$ the torsion\npart of the degree zero part of the Chow group of zero cycl
es. For a curve\n$X\,$ this isomorphism agrees with the Abel-Jacobi isomor
phism\n$CH^1(X)_{alg}\\longrightarrow Pic_X(k)\,$ where $CH^1(X)_{alg}$ is
the\nsubgroup of $CH^1(X)$ consisting of algebraically trivial cycles and
\n$Pic_X$ is the Picard variety.\n\nTo extend this picture to other Chow g
roups\, Samuel introduced the concept\nof regular homomorphisms. For divis
ors and zero cycles\, the map $alb_X$\nand the Abel-Jacobi isomorphism are
universal with respect to regular\nhomomorphisms. The case of codimension
$2$ cycles was also treated by\nMurre.\n\nIn this talk\, we explain how t
o extend this picture to other motivic\ninvariants. If time permits\, we e
xplain the relation with Griffiths's\nintermediate Jacobians.\n\nhttps://i
ndico.tifr.res.in/indico/conferenceDisplay.py?confId=6027
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6027
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arithmetic geometry of toric varieties
DTSTART;VALUE=DATE-TIME:20171130T103000Z
DTEND;VALUE=DATE-TIME:20171130T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6047@cern.ch
DESCRIPTION:Abstract:\n\nWe will present results obtained in collaboration
with J.Burgos and\nM.Sombra. These extend the well known dictionary betwe
en the geometric\nproperties of toric varieties and convex geometry. In pa
rticular\, we give\ncombinatorial descriptions of classical invariants of
arithmetic geometry\,\nsuch as metric\, height\, essential minimum\, posit
ivity properties and\nequidistribution.\n\nhttps://indico.tifr.res.in/indi
co/conferenceDisplay.py?confId=6047
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6047
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Infinite dimensional superalgebras and their representations'
DTSTART;VALUE=DATE-TIME:20171207T103000Z
DTEND;VALUE=DATE-TIME:20171207T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6062@cern.ch
DESCRIPTION:Abstract:\n\nWe will discuss examples\, classification and rep
resentations of \nsome infinite dimensional super algebras that arise in P
hysics.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6
062
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6062
END:VEVENT
BEGIN:VEVENT
SUMMARY:"Two invariants related to two conjectures due to Nagata"
DTSTART;VALUE=DATE-TIME:20171214T103000Z
DTEND;VALUE=DATE-TIME:20171214T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6085@cern.ch
DESCRIPTION:Abstract:\n\nSeshadri's constant is related to a conjecture du
e to Nagata. Another\nconjecture\, also due to Nagata and solved by Bombie
ri in 1970\, is related\nwith algebraic values of meromorphic functions. T
he main part of\nBombieri's proof leads to a Schwarz Lemma in several vari
ables\, the proof\nof which gives rise to another invariant associated wit
h symbolic powers\nof the ideal of functions vanishing on a finite set of
points. This\ninvariant is an asymptotic measure of the least degree of a
polynomial in\nseveral variables with given order of vanishing on a finite
set of points.\nRecent works on the resurgence of ideals of points and th
e containment\nproblem compare powers and symbolic powers of ideals.\n\nht
tps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6085
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6085
END:VEVENT
BEGIN:VEVENT
SUMMARY:'p-adic symmetric spaces'
DTSTART;VALUE=DATE-TIME:20171221T103000Z
DTEND;VALUE=DATE-TIME:20171221T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6109@cern.ch
DESCRIPTION:Abstract:\nIn his ICM talk in Nice in 70 Grothendieck asked wh
at is the image of the\np-adic analog of Griffith's period mapping as a su
bset of a flag variety?\nWe now can give an answer by interpreting those p
eriod mappings in terms\nof modifications of vector bundles on the curve (
a p-adic analog of\nSimpson's Twistor structures).\nI will explain a recen
t result obtained jointly with Miaofen Chen and Xu\nShen that allows us to
compute those period spaces in some particular\ncases. For example\nwe ca
n compute the p-adic period space for polarized K3 surfaces with\nsupersin
gular reduction.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py
?confId=6109
LOCATION:TIFR\, Mumbai AG 69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6109
END:VEVENT
BEGIN:VEVENT
SUMMARY:"Extension of Mixed Hodge structures and Special values of Hyperge
ometric functions"
DTSTART;VALUE=DATE-TIME:20180104T103000Z
DTEND;VALUE=DATE-TIME:20180104T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6122@cern.ch
DESCRIPTION:Abstract :\nIn this talk we discuss certain extensions of mixe
d Hodge structures which\nare coming from the mixed Hodge structure on cer
tain graded quotients of\nthe group ring of the Fundamental group of a smo
oth projective pointed\ncurve. Such extensions are computed using iterated
integrals. In a very\nspecial case those iterated integral evaluated as a
special values of\nhypergeometric functions.\n\nhttps://indico.tifr.res.i
n/indico/conferenceDisplay.py?confId=6122
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6122
END:VEVENT
BEGIN:VEVENT
SUMMARY:'Extension of Mixed Hodge structures and Special values of Hyperge
ometric functions'
DTSTART;VALUE=DATE-TIME:20180104T103000Z
DTEND;VALUE=DATE-TIME:20180104T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6127@cern.ch
DESCRIPTION:Abstract:\n\nIn this talk we discuss certain extensions of mix
ed Hodge structures which\nare coming from the mixed Hodge structure on ce
rtain graded quotients of\nthe group ring of the Fundamental group of a sm
ooth projective pointed\ncurve. Such extensions are computed using iterate
d integrals. In a very\nspecial case those iterated integral evaluated as
a special values of\nhypergeometric functions.\n\nhttps://indico.tifr.res.
in/indico/conferenceDisplay.py?confId=6127
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6127
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kahler-Einstein metrics on Fano manifolds
DTSTART;VALUE=DATE-TIME:20180111T103000Z
DTEND;VALUE=DATE-TIME:20180111T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6149@cern.ch
DESCRIPTION:Abstract - The uniformization theorem states that any compact
Riemann surface admits a metric of constant curvature. A deep and importan
t problem in complex geometry is to characterize Kahler manifolds admittin
g constant scalar curvature Kahler (cscK) metrics or extremal Kahler metri
cs. Even in the special case of Kahler-Einstein metrics\, starting with th
e work of Yau and Aubin in the 1970's\, a complete solution was obtained o
nly very recently by Chen-Donaldson-Sun (and Tian). Their main results say
s that a Fano manifold admits a Kahler-Einstein metric if and only if it i
s K-stable. I will survey some of these recent developments\, and then foc
us on a refinement obtained in collaboration with Gabor Szekelyhidi. This
has led to the discovery of new Kahler-Einstein manifolds. If time permits
\, I will also talk about some open problems on constructing cscK and extr
emal metrics on blow-ups of extremal manifolds\, and mention some recent p
rogress.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
6149
LOCATION:TIFR\, MUMBAI AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6149
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Rigidity\, nonlinear flows and optimal symmetry for extremals of
functional inequalities'
DTSTART;VALUE=DATE-TIME:20180123T060000Z
DTEND;VALUE=DATE-TIME:20180123T070000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6185@cern.ch
DESCRIPTION:Abstract:\nThe analysis of optimality and symmetry properties
of extremals in\nfunctional inequalities has been performed recently by in
troducing nonlinear flows into the picture. These results solve conjecture
s about symmetry and symmetry breaking in functional inequalities which pl
ay an important role in various areas of analysis. Also\, as a consequence
we have obtained optimal estimates for the principal eigenvalues of linea
r operators and rigidity results of solutions of nonlinear elliptic PDEs f
or compact and noncompact in Riemaniann manifolds.\n\nThis work has been d
one in collaboration with J. Dolbeault and M. Loss\n\nhttps://indico.tifr.
res.in/indico/conferenceDisplay.py?confId=6185
LOCATION:TIFR\, Mumbai AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6185
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Hodge theory and unitary representations of reductive groups'
DTSTART;VALUE=DATE-TIME:20180125T103000Z
DTEND;VALUE=DATE-TIME:20180125T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6186@cern.ch
DESCRIPTION:Abstract:\nUnderstanding the irreducible unitary representatio
ns of reductive Lie\ngroups is the major remaining problem in the represen
tation theory of such\ngroups. I shall describe an algebraic-geometric app
roach to the study of\ntheir unitary representations. This is joint work w
ith Kari Vilonen.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.p
y?confId=6186
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6186
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Making a Global Mathematician'
DTSTART;VALUE=DATE-TIME:20180208T103000Z
DTEND;VALUE=DATE-TIME:20180208T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6207@cern.ch
DESCRIPTION:Abstract:\nBetween 1947 and 1950\, French mathematician Lauren
t Schwartz went from being virtually unknown outside of France to an inter
national mathematical celebrity. By the mid-1950s\, he was a famed world t
raveler\, lecturing in such varied places as Buenos Aires\, Tunisia\, and
the TIFR. Schwartz's emergence as a global mathematician followed a patter
n that would have been virtually unthinkable to a prior generation\, but b
ecame increasingly possible for later generations of mathematicians. I wil
l discuss Schwartz's trajectory in the context of mathematicians' changing
discipline in the mid-twentieth century\, as well as aspects of Schwartz'
s theories\, personality\, and politics that shaped is course. This story
shall illustrate several broader claims I am developing about the history
of mathematics in the mid-twentieth century\, and will explain\, in partic
ular\, why I have been so keenly looking forward to my research in the TIF
R archives.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?conf
Id=6207
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6207
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Cayley groups'
DTSTART;VALUE=DATE-TIME:20180215T103000Z
DTEND;VALUE=DATE-TIME:20180215T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6220@cern.ch
DESCRIPTION:Abstract:\n I will start the talk from the classical "Cayley t
ransform" for the special orthogonal group SO(n) defined by Arthur Cayley
in 1846. A connected linear algebraic group G over C is called a *Cayley g
roup* if it admits a *Cayley map*\, that is\, a G-equivariant birational i
somorphism between the group variety G and its Lie algebra Lie(G). For exa
mple\, SO(n) is a Cayley group. A linear algebraic group G is called *sta
bly Cayley* if G x S is Cayley for some torus S. I will consider semisimpl
e algebraic groups\, in particular\, simple algebraic groups. I will descr
ibe classification of Cayley simple groups and of stably Cayley semisimple
groups. (Based on joint works with Boris Kunyavskii and others.)\n\nhttps
://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6220
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6220
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Hausdorff dimension in inhomogeneous Diophantine approximation'
DTSTART;VALUE=DATE-TIME:20180222T103000Z
DTEND;VALUE=DATE-TIME:20180222T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6246@cern.ch
DESCRIPTION:Abstract:\nHomogeneous dynamics is often helpful to solve some
problems in number\ntheory. We will explain a particular example of the s
etting in homogeneous\ndynamics\, useful for Diophantine approximation. We
will then show why the\nset of epsilon-badly approximable target vectors
in inhomogeneous\nDiophantine approximation is not full for almost every a
pproximating\nvectors. We further explain the situation in dimension 1\, w
hich is almost\nsettled with the aid of continued fraction expansions. The
main part is a\njoint work with Uri Shapira and Nicolas de Saxce.\n\nhttp
s://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6246
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6246
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Syzygies\, Tropical Geometry and Algebraic Curves'
DTSTART;VALUE=DATE-TIME:20180308T103000Z
DTEND;VALUE=DATE-TIME:20180308T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6277@cern.ch
DESCRIPTION:Abstract:\nThe Riemann-Roch theorem is fundamental to algebrai
c geometry.\nIn 2006\, Baker and Norine discovered an analogue of the Riem
ann-Roch\n theorem for graphs. In fact\, this theorem is not a mere analog
ue but has\nconcrete relations with its algebro-geometric counterpart. Sin
ce its\n conception this topic has been explored in different directions\,
two\nsignificant directions are i. Connections to topics in discrete geom
etry\n and commutative algebra ii. As a tool to studying linear series on\
nalgebraic curves. We will provide a glimpse of these developments. This\n
talk is based on joint work with i. Omid Amini\, ii. Bernd Sturmfels\, iii
.\nFrank-Olaf Schreyer and John Wilmes.\n\nhttps://indico.tifr.res.in/indi
co/conferenceDisplay.py?confId=6277
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6277
END:VEVENT
BEGIN:VEVENT
SUMMARY:`Periodic monopoles and difference modules'
DTSTART;VALUE=DATE-TIME:20180315T103000Z
DTEND;VALUE=DATE-TIME:20180315T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6289@cern.ch
DESCRIPTION:Abstract:\nIn 1960's\, Narasimhan and Seshadri proved that\na
holomorphic vector bundle on a compact Riemann surface\nis stable if and o
nly if it is induced by an irreducible unitary\nflat bundle. Since then\,
many generalizations and variants have been\nstudied. In particular\, Simp
son proved the equivalence of\nirreducible tame harmonic bundles\,\nstable
parabolic bundles with logarithmic connections\nand stable parabolic bund
les with logarithmic Higgs fields\non compact punctured Riemann surfaces.\
n\nIn this talk\, we shall explain a variant of Simpson's theorem\nin the
context of periodic monopoles and difference modules\,\nthat is the equiva
lence between singular periodic monopoles of GCK type\nand stable paraboli
c difference modules.\n\nhttps://indico.tifr.res.in/indico/conferenceDispl
ay.py?confId=6289
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6289
END:VEVENT
BEGIN:VEVENT
SUMMARY:An Automorphic translation of Deligne's conjecture: Special values
of L-functions for GL(n) x GL(m) over a number field.
DTSTART;VALUE=DATE-TIME:20180405T103000Z
DTEND;VALUE=DATE-TIME:20180405T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6339@cern.ch
DESCRIPTION:Abstract:\n\n In the talk I will discuss algebraicity results
for all the critical\nvalues of certain Rankin--Selberg L-functions for GL
(n) x GL(m) over a\nnumber field. These results are derived from the theor
y of L-functions by\ngiving a cohomological interpretation to an integral
representing a\ncritical L-value in terms of Poincare pairing.\n\nhttps://
indico.tifr.res.in/indico/conferenceDisplay.py?confId=6339
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6339
END:VEVENT
BEGIN:VEVENT
SUMMARY:`On the Ramanujan-Petersson conjecture for modular forms of half-i
ntegral weight'
DTSTART;VALUE=DATE-TIME:20180411T060000Z
DTEND;VALUE=DATE-TIME:20180411T070000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6348@cern.ch
DESCRIPTION:Abstract:\nWe shall discuss the Ramanujan-Petersson conjecture
for the growth\nof the Fourier coefficients of cusp forms of half-integra
l weight. We will\nshow that the predicted estimate is optimal (joint work
with S. Gun\,\n2018).\n\nhttps://indico.tifr.res.in/indico/conferenceDisp
lay.py?confId=6348
LOCATION:TIFR\, Mumbai AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6348
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dynamics of Schwarz reflections: mating polynomials with groups
DTSTART;VALUE=DATE-TIME:20180607T103000Z
DTEND;VALUE=DATE-TIME:20180607T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6455@cern.ch
DESCRIPTION:Abstract:\nA domain in the complex plane is called a quadratur
e domain if it admits a\nglobal Schwarz reflection map. Topology of quadra
ture domains has\nimportant applications to physics\, and is intimately re
lated to iteration\nof Schwarz reflection maps.\n\nWe will look at a speci
fic one-parameter family of Schwarz reflection\nmaps\, and show that every
post-critically finite map in this family arises\nas the mating of a post
-critically finite quadratic anti-holomorphic\npolynomial and the ideal tr
iangle group. Time permitting\, we will also\ndescribe a combinatorial mod
el for the ``connectedness locus'' of this\nfamily.\n\nJoint work with Seu
ng-Yeop Lee\, Mikhail Lyubich\, and Nikolai Makarov.\n\nhttps://indico.tif
r.res.in/indico/conferenceDisplay.py?confId=6455
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6455
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sub-convexity problems: Some history and recent developments
DTSTART;VALUE=DATE-TIME:20180823T103000Z
DTEND;VALUE=DATE-TIME:20180823T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6575@cern.ch
DESCRIPTION:Abstract:\nBounding automorphic $L$-functions on the critical
line $\\text{Re}(s) =\n1/2$ is a central problem in the analytic theory o
f $L$-functions. The\nfunctional equation and the Phragmen-Lindel{\\" o}f
principle from complex\nanalysis yield the convexity bound $L(1/2+it\,\\pi
)\\ll\nC(\\pi\,t)^{1/4+\\varepsilon}$ where $C(\\pi\,t)$ is the ``analytic
conductor"\nof the $L$-function. Lindel{\\" o}f hypothesis\, which is a c
onsequence of\nthe Grand Riemann Hypothesis (GRH)\, predicts that the bo
und\n$C(\\pi\,t)^\\varepsilon$ for any $\\varepsilon>0$. Any bound with ex
ponent\nsmaller than $1/4$ is called a sub-convexity bound. In this contex
t the\nWeyl exponent $1/6$\, which is one-third of the way down from conve
xity\ntowards Lindel{\\" o}f\, is a known barrier which has been achieved
only for\na handful of families. First sub-convexity bound is proved by\nH
ardy-Littlewood and Weyl independently for the Riemann zeta function.\n\n
\nIn this talk we shall talk about some recent developments and new\ntechn
iques. This talk is meant for a general audience and we shall be\nexplicit
ly defining the relevant terms.\n\nhttps://indico.tifr.res.in/indico/confe
renceDisplay.py?confId=6575
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6575
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gauss hypergeometric functions and Lauricella Functions.
DTSTART;VALUE=DATE-TIME:20180830T103000Z
DTEND;VALUE=DATE-TIME:20180830T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6596@cern.ch
DESCRIPTION:Abstract:\nA brief review of some results of Beukers-Heckman a
nd of Deligne-Mostow\nwill be given. Some recent related work will also be
recalled.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confI
d=6596
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6596
END:VEVENT
BEGIN:VEVENT
SUMMARY:Locally analytic group action on the Lubin-Tate moduli space.
DTSTART;VALUE=DATE-TIME:20180906T103000Z
DTEND;VALUE=DATE-TIME:20180906T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6597@cern.ch
DESCRIPTION:Abstract: The Lubin-Tate moduli space X is a p-adic analytic o
pen unit\ndisc which parametrizes deformations of a formal group H defined
over an\nalgebraically closed field of characteristic p. The natural acti
on of the\ngroup Aut(H) on X is highly non-trivial\, and gives rise to cer
tain p-adic\nrepresentations known as 'locally analytic' representations o
n the dual\nvector space of global sections over X. In this talk\, I will
first\nintroduce the geometric object X\, then speak about aforementioned\
nrepresentations\, and then compare them with the well-studied example of\
nlocally analytic representations arising from the p-adic upper half plane
.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6597
LOCATION:TIFR\, Mumbai AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6597
END:VEVENT
BEGIN:VEVENT
SUMMARY:Components of harmonic Poincare duals of special cycles
DTSTART;VALUE=DATE-TIME:20180927T103000Z
DTEND;VALUE=DATE-TIME:20180927T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6628@cern.ch
DESCRIPTION:Abstract: The de Rham complex of a compact locally symmetric s
pace \\Gamma\\ G /K is isometric to the cochain complex C*(g\,K\; C^\\inft
y(\\Gamma\\ G)_K) of the relative Lie algebra cohomology of (g\,K) with co
efficients in C^\\infty(\\Gamma\\ G)_K. This gives an orthogonal decomposi
tion of the space of harmonic forms on \\Gamma\\ G /K into cochain groups
of the form C*(g\,K\;V)\, where V is an isotropical sub-represebtation of
C^\\infty(\\Gamma\\ G)_K on which the Casimir operator acts trivially. Usi
ng representation theoretic methods\, we will deduce some conditions for v
anishing of a component of the harmonic Poincare dual of a special cycle \
\Gamma'\\ G' /K'$ with respect to this decomposition. For certain special
cycles\, when G=SU(p\,q)\, these conditions can be applied to deduce whic
h components do not vanish.\n\nhttps://indico.tifr.res.in/indico/conferenc
eDisplay.py?confId=6628
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6628
END:VEVENT
BEGIN:VEVENT
SUMMARY:Congruence Subgroup Problem\; A Survey.
DTSTART;VALUE=DATE-TIME:20181011T103000Z
DTEND;VALUE=DATE-TIME:20181011T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6662@cern.ch
DESCRIPTION:Abstract:\nThis talk will be a survey on the developments of t
he congruence\nsubgroup problem over number fields since the paper of Bass
-Milnor-Serre\nin 1970.\n\nhttps://indico.tifr.res.in/indico/conferenceDis
play.py?confId=6662
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6662
END:VEVENT
BEGIN:VEVENT
SUMMARY:Spin geometry in Kac-Moody theory
DTSTART;VALUE=DATE-TIME:20181018T103000Z
DTEND;VALUE=DATE-TIME:20181018T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6668@cern.ch
DESCRIPTION:Abstract:\nIn this expository lecture we concisely introduce\n
spin manifolds and investigate their appearance in\nthe literature along w
ith their connections to other\nbranches of mathematics. Then very briefly
explain\nthe general idea of a symmetric space obtained from\na split Kac
-Moody group and how one can develop spin\ngeometry in this context.\n\nht
tps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6668
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6668
END:VEVENT
BEGIN:VEVENT
SUMMARY:Certain identities among eigenforms.
DTSTART;VALUE=DATE-TIME:20181025T103000Z
DTEND;VALUE=DATE-TIME:20181025T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6677@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
6677
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6677
END:VEVENT
BEGIN:VEVENT
SUMMARY:A triangulated approach to the Bloch-Beilinson filtration
DTSTART;VALUE=DATE-TIME:20181101T103000Z
DTEND;VALUE=DATE-TIME:20181101T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6704@cern.ch
DESCRIPTION:Abstract: We will present an approach to the Bloch-Beilinson f
iltration in the context of Voevodsky’s triangulated category of motives
where the truncation functors are triangulated.\n\nhttps://indico.tifr.re
s.in/indico/conferenceDisplay.py?confId=6704
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6704
END:VEVENT
BEGIN:VEVENT
SUMMARY:"Revisiting Johannson’s Deformation Theorem"
DTSTART;VALUE=DATE-TIME:20181108T103000Z
DTEND;VALUE=DATE-TIME:20181108T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6713@cern.ch
DESCRIPTION:Abstract: Jaco-Shalen and Johannson developed in 1979\, what
are now called JSJ decompositions\, for Haken manifolds with incompressibl
e boundary. This decomposes the three manifold into Canonical simple piece
s and fibered pieces. Johannson also proved that any homotopy equivalence
between two such Haken manifolds can be deformed to carry simple pieces to
simple pieces and fibered pieces to fibered pieces. Scott and Swarup deve
loped recently a similar decomposition for Poincare Duality pairs of dimen
sions n+2\, n>0 (think of these as aspherical manifolds with incompressibl
e boundary). We show now that any isomorphism in the fundamental groups b
etween two Poincare Duality pairs has the same property\, that is\, it is
independent of the boundary structure. The theory involves the so called a
lmost invariant sets over virtually polycyclic groups\, which correspond t
o immersions over annuli and tori in the three dimensional case. This is j
oint work with Lawrence Reeves and Peter Scott.\n\nhttps://indico.tifr.res
.in/indico/conferenceDisplay.py?confId=6713
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6713
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mod p representations of GL(2\,F)
DTSTART;VALUE=DATE-TIME:20181115T103000Z
DTEND;VALUE=DATE-TIME:20181115T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6724@cern.ch
DESCRIPTION:Abstract:\nMod $p$ representation theory of $p$-adic reductive
groups originated with the work of Barthel and Livne from the mid ninetie
s where they studied irreducible smooth mod $p$ representations of $GL(2\,
F)$. Though there has been a lot of recent progress\, a complete classific
ation of all smooth mod $p$ representations of $G(F)$ is achieved only in
very few cases\, essentially when $G=GL(2)$ or one of its variants and whe
n $F=Q_p$. The case of $GL(2\,Q_p)$ follows from the works of Barthel-Livn
e and Breuil. In this talk we will survey the case of $GL(2\,Q_p)$ and ind
icate an approach to study this question for $GL(2\,F)$ where $F$ is an un
ramified extension of $Q_p$. This latter work is joint with Arindam Jana.\
n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6724
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6724
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Holomorphic Sectional Curvature and Fibration
DTSTART;VALUE=DATE-TIME:20181122T103000Z
DTEND;VALUE=DATE-TIME:20181122T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6728@cern.ch
DESCRIPTION:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=
6728
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6728
END:VEVENT
BEGIN:VEVENT
SUMMARY:On Holomorphic Sectional Curvature and Fibration
DTSTART;VALUE=DATE-TIME:20181122T103000Z
DTEND;VALUE=DATE-TIME:20181122T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6729@cern.ch
DESCRIPTION:Abstract\nA fibration\, loosely speaking\, is generalization o
f the concept of a fiber bundle. For a given fibration\, we can talk about
its two “directions”: base and fibers. Suppose we are given
Hermitian metrics on the base and fibers of a holomorphic fibration su
ch that the holomorphic sectional curvatures have same signs on the base a
nd fibers. Then\, we show that the given metrics in the two “directions
” can be used to construct a warped product metric on the total space su
ch that this metric has the same sign of the holomorphic sectional curvatu
re on the total space as that of the given metrics on the base and fibers.
The case of negative holomorphic sectional curvature was proved by Cheun
g in 1989. In this talk\, we shall focus on the positive holomorphic sect
ional curvature case.\n\nhttps://indico.tifr.res.in/indico/conferenceDispl
ay.py?confId=6729
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6729
END:VEVENT
BEGIN:VEVENT
SUMMARY:Universal deformations of dihedral representations
DTSTART;VALUE=DATE-TIME:20181129T103000Z
DTEND;VALUE=DATE-TIME:20181129T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6749@cern.ch
DESCRIPTION:Abstract: Given a 2-dimensional dihedral representation of a p
rofinite\ngroup over a finite field\, we will give necessary and sufficien
t\nconditions for its universal deformation to be dihedral. We will then\n
specialize to the case of absolute Galois group of a number field and give
\nsufficient conditions for the universal deformation unramified outside a
\nfinite set of primes to be dihedral. We will also see its applications t
o\nunramfied Fontaine-Mazur conjecture and to an R=T theorem (in the spiri
t\nof Calegari-Geraghty) in the setting of Hilbert modular forms of parall
el\nweight one. We will begin with a brief introduction to the deformation
\ntheory of Galois representations. This talk is based on joint work with\
nGabor Wiese.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?co
nfId=6749
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6749
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some unpublished work of Harish-Chandra
DTSTART;VALUE=DATE-TIME:20181206T103000Z
DTEND;VALUE=DATE-TIME:20181206T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6758@cern.ch
DESCRIPTION:Abstract:\nWhen Harish-Chandra died in 1983\, he left behind a
voluminous pile of\nhandwritten manuscripts on harmonic analysis on semis
imple Lie groups over\nreal/complex and p-adic fields. The manuscripts wer
e turned over to the\narchives of the Institute for Advanced Study at Prin
ceton\, and are archived\nthere.\n\nRobert Langlands is the Trustee of the
Harish- Chandra archive\, and has\nalways been interested in finding a wa
y of salvaging whatever might be\nvaluable in these manuscripts. Some year
s ago\, at a conference in UCLA\, he\nasked if V. S. Varadarajan and I mig
ht look at some of these.\n\nThe results of our efforts have resulted in t
he publication of the Volume 5\n(Posthumous) of the Collected works of Har
ish-Chandra by Springer Verlag.\nMy talk will be devoted to a bare outline
of the results in this volume\,\nwithout much detail.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=6758
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6758
END:VEVENT
BEGIN:VEVENT
SUMMARY:Reduced Whitehead groups of algebras.
DTSTART;VALUE=DATE-TIME:20181220T103000Z
DTEND;VALUE=DATE-TIME:20181220T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6793@cern.ch
DESCRIPTION:Abstract:\nAny central simple algebra A over a field K is a fo
rm of a matrix algebra.\nFurther A/K comes equipped with a reduced norm ma
p which is obtained by\ntwisting the determinant function. Every element i
n the commutator\nsubgroup [A*\, A*] has reduced norm 1 and hence lies in
SL_1(A)\, the group\nof reduced norm one elements of A. Whether the rever
se inclusion holds was\nformulated as a question in 1943 by Tannaka and Ar
tin in terms of the\ntriviality of the reduced Whitehead group SK_1(A) :=
SL_1(A)/[A*\,A*].\n\nOne can define Whitehead groups more generally for an
y isotropic group and\nit turns out that the Tannaka-Artin question is a s
pecial case of the\nwell-known Kneser-Tits conjecture. The Whitehead group
detects the\nnon-rationality of the underlying variety of the algebraic g
roup and\ntherefore is an interesting albeit difficult invariant to study.
In this\ntalk\, we discuss these connections to rationality questions and
trace the\nprogress towards answering the Tannaka-Artin question\, which
becomes\nespecially interesting over low cohomological dimension fields.\n
\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6793
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6793
END:VEVENT
BEGIN:VEVENT
SUMMARY:F-rationality of Rees algebras.
DTSTART;VALUE=DATE-TIME:20181227T103000Z
DTEND;VALUE=DATE-TIME:20181227T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6807@cern.ch
DESCRIPTION:Abstract:\nWe define notion of F-rational rings (introduced by
Fedder and\nWatanabe). Then we will discuss F-rationality of Rees algebra
s.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6807
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6807
END:VEVENT
BEGIN:VEVENT
SUMMARY:Conformal blocks for Galois covers of algebraic curves
DTSTART;VALUE=DATE-TIME:20190103T103000Z
DTEND;VALUE=DATE-TIME:20190103T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6815@cern.ch
DESCRIPTION:Abstract: This is a joint work with Jiuzu Hong. We study the s
paces of twisted conformal blocks attached to A-curves S with marked A-orb
its and an action of A on a simple Lie algebra g\, where A is a finite gro
up. We prove that if A stabilizes a Borel subalgebra of g\, then Propogati
on Theorem and Factorization Theorem hold. We endow a projectively flat co
nnection on the sheaf of twisted conformal blocks attached to a smooth fam
ily of pointed A-curves\; in particular\, it is locally free. We also prov
e that the sheaf of twisted conformal blocks on the stable compactificatio
n of Hurwitz stack is locally free. We further identify the space of twist
ed conformal blocks with the space of global sections of certain line bund
les on the stack of A-equivariant principal G-bundles over the curve S\, G
being the simply-connected group with Lie algebra g. This generalizes the
Verlinde theory of conformal blocks to the twisted setting.\n\nhttps://in
dico.tifr.res.in/indico/conferenceDisplay.py?confId=6815
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6815
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asymptotic estimates on the geometry of Laplace eigenfunctions
DTSTART;VALUE=DATE-TIME:20190110T103000Z
DTEND;VALUE=DATE-TIME:20190110T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6837@cern.ch
DESCRIPTION:Abstract: Given a closed smooth Riemannian manifold M\, the La
place operator is known to possess a discrete spectrum of eigenvalues goin
g to infinity. We are interested in the properties of the nodal sets and n
odal domains of corresponding eigenfunctions in the high energy (semiclass
ical) limit. We focus on some recent results on the size of nodal domains
and tubular neighbourhoods of nodal sets of such high energy eigenfunction
s (joint work with Bogdan Georgiev).\n\nhttps://indico.tifr.res.in/indico/
conferenceDisplay.py?confId=6837
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6837
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mirror symmetry and Lagrangian Floer cohomology
DTSTART;VALUE=DATE-TIME:20190117T103000Z
DTEND;VALUE=DATE-TIME:20190117T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6858@cern.ch
DESCRIPTION:Abstract: Mirror symmetry predicts a duality between \ncomple
x and symplectic geometry. In particular the conjecture\nrelates (in Kont
sevich's version) sheaf cohomology of vector bundles with Floer theory of
Lagrangian submanifolds. I will discuss some of the ideas behind the conj
ecture\, such as the definition of a Lagrangian submanifold\, and some rec
ent work on the mirror analog of deformation of vector bundles which\, as
suggested by Fukaya-Oh-Ono-Ohta\, corresponds to smoothing singularities o
f the Lagrangians.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.
py?confId=6858
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6858
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gradient flows of geometric variational problems: the elastic curv
e flow.
DTSTART;VALUE=DATE-TIME:20190124T103000Z
DTEND;VALUE=DATE-TIME:20190124T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6863@cern.ch
DESCRIPTION:Abstract: \nWhen considering a variational problem\, one is i
nterested in its minimizers\, and more generally\, its critical points giv
en by the Euler-Lagrange equation. The critical points are typically speci
al geometries -- Einstein metrics\, Yang-Mills fields\, harmonic maps\, el
astic membranes etc. -- and one would like to flow a generic initial geome
try to a terminal special geometry. This is usually accomplished by consid
ering the gradient flow of the functional under consideration. The definit
ion of the gradient requires a choice of (Riemannian) metric on the domain
of the functional\, which to a large extent determines the analytical pro
perties of the gradient flow. \n\nIn this lecture\, we will discuss these
issues in the simplest example of closed real curves in the Euclidean plan
e under the influence of the elastic energy\, the average squared curvatur
e of the curve. The critical points are the so-called elastica found by Le
onard Euler in a beautiful paper of 1744. The usual gradient flow with res
pect to the variational $L^2$ metric is a 4th order non-linear parabolic P
DE requiring hard analysis. We show that by using a geometrically defined
metric\, the gradient flow becomes an ODE on a Hilbert manifold\, whose lo
ngtime existence and convergence to elastica requires nothing more than el
ementary ODE theory. We will intersperse the talk with numerical experimen
ts carried out via this approach.\n\nhttps://indico.tifr.res.in/indico/con
ferenceDisplay.py?confId=6863
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6863
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brauer group of moduli of torsors under Bruhat-Tits group scheme $
\\mathcal{G}$ over a curve.
DTSTART;VALUE=DATE-TIME:20190131T103000Z
DTEND;VALUE=DATE-TIME:20190131T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6885@cern.ch
DESCRIPTION:Abstract:\nLet X be a smooth projective curve over the field o
f complex numbers. We\ncompute the Brauer group of the moduli stack and th
e regularly stable\nlocus of the moduli space of $\\mathcal{G}$-torsors on
X.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6885
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6885
END:VEVENT
BEGIN:VEVENT
SUMMARY:Derived category of moduli of vector bundles on curves.
DTSTART;VALUE=DATE-TIME:20190207T103000Z
DTEND;VALUE=DATE-TIME:20190207T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6909@cern.ch
DESCRIPTION:Abstract:\nThe bounded category of a smooth variety is an impo
rtant invariant that\nhas applications to various areas of mathematics. De
composing a derived\ncategory into simpler triangulated sub categories is
a fundamental\nquestion. Fano varieties always admits a non trivial semior
thogonal\ndecomposition. A natural class of Fano varieties come from the m
oduli\nspace of vector bundles of on a curve with fixed determinant and c
oprime\ndegree. In this talk\, we will discuss natural subcategories of th
e derived\ncategory of these moduli spaces and give a conjectural semiort
hogonal\ndecomposition in rank 2 and provide evidence towards the conjectu
re.\n\nThis is a joint work with Pieter Belmans and Sergey Galkin.\n\nhtt
ps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6909
LOCATION: AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6909
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the Hot spots conjecture for Euclidean triangles.
DTSTART;VALUE=DATE-TIME:20190214T103000Z
DTEND;VALUE=DATE-TIME:20190214T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6921@cern.ch
DESCRIPTION:Abstract:\nLet U be a convex subset of the Euclidean plane wit
h piecewise\nsmooth boundary. The Hot spots conjecture due to J. Rauch say
s that a\nglobal maxima of a second Neumann eigenfunction of U does not li
e in the\ninterior of U. In this talk I will give a brief survey of the kn
own\nresults and explain a new geometric approach that can be used to reco
ver\nsome of the known results in an unified way. These results are part o
f an\non going joint project with Chris Judge.\n\nhttps://indico.tifr.res.
in/indico/conferenceDisplay.py?confId=6921
LOCATION: AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6921
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dynamics of 2-interval piecewise linear contraction maps and Hecke
-Mahler series
DTSTART;VALUE=DATE-TIME:20190221T103000Z
DTEND;VALUE=DATE-TIME:20190221T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-6932@cern.ch
DESCRIPTION:Abstract: Let $I=[0\,1)$ be the unity interval. Let $0A_g gives an immersion (
outside the hyperelliptic locus) of the moduli space of complex curves of
genus g into the moduli space of principally polarized abelian varieties
of dimension g. We study the local geometry of this immersion by means of
the natural riemannian (orbifold) structure induced on A_g from Siegel sp
ace. In particular two methods to give a bound on the dimension of the tot
ally geodesic subvarieties of A_g contained in M_g are discussed. The firs
t one (Colombo-Frediani-Ghigi) uses the second fundamental form associated
to the Torelli immersion and the second one (Ghigi-P-Torelli) uses instea
d a sort of local Fujita decomposition along geodesics. We recall that the
Shimura varieties are (algebraic) totally geodesic subvarieties of A_g an
d for g>>0\, according to the Coleman-Oort conjecture\, they should not b
e contained in t(M_g) .\n\nhttps://indico.tifr.res.in/indico/conferenceDis
play.py?confId=7027
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7027
END:VEVENT
BEGIN:VEVENT
SUMMARY:The geometry of Kac-Moody groups
DTSTART;VALUE=DATE-TIME:20190418T103000Z
DTEND;VALUE=DATE-TIME:20190418T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7054@cern.ch
DESCRIPTION:Abstract:\nKac and Peterson introduced a topology on real Kac-
Moody\ngroups that is very suitable for their study. Hartnick\, K. and Mar
s\nproved that this topology turns their twin building into a topological\
ntwin building in the sense of Kramer. More recently\, Freyn\, Hartnick\,\
nHorn\, K. constructed Kac-Moody symmetric spaces that share many\npropert
ies with Riemannian symmetric spaces but also allow for new\nfeatures such
as their twin building at infinity\, one into a future\ndirection\, the o
ther into a past direction.\n\nIt is my firm belief that this Kac-Moody sy
mmetric space is the\nnatural geometry for the further study of arithmetic
Kac-Moody groups\n-- the geometry of the twin building seems a little spa
rse\, although\nit still was sufficient for Farahmand Parsa\, Horn\, K. to
establish\nstrong rigidity and superrigidity properties of arithmetic Kac
-Moody\ngroups.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?
confId=7054
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7054
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lengths on Free groups
DTSTART;VALUE=DATE-TIME:20200116T103000Z
DTEND;VALUE=DATE-TIME:20200116T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7588@cern.ch
DESCRIPTION:Abstract:\nTerence Tao posted on his blog a question of Apoorv
a Khare\,\nasking whether the free group on two generators has a length\nf
unction $l:F_2→R$ which is homogeneous\, i.e.\, such that\n$l(g^n)=n l(g
)$. A week later\, the problem was solved by an\nactive collaboration of s
everal mathematicians (with a little help\nfrom a computer) through Tao’
s blog. In fact a more general result\nwas obtained\, namely that any homo
geneous length function on a\ngroup $G$ factors through its abelianization
$G/[G\,G]$.\nI will discuss the proof of this result and also the process
of\ndiscovery.\n\nThe unusual feature of the use of computers here was\nt
hat a computer generated but human readable proof was read\,\nunderstood\,
generalized and abstracted by mathematicians to\nobtain the key lemma in
an interesting mathematical result -\nperhaps the first such instance.\n\n
I will also discuss conjugacy-invariant lengths on free groups and\nan ext
ension of the main result to quasi-homogeneous lengths.\n\nhttps://indico.
tifr.res.in/indico/conferenceDisplay.py?confId=7588
LOCATION: AG69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7588
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the decimal expansion of $\\log (2020/2019)$ and $e$.
DTSTART;VALUE=DATE-TIME:20200213T103000Z
DTEND;VALUE=DATE-TIME:20200213T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7645@cern.ch
DESCRIPTION:Abstract: It is commonly expected that $e$\, $\\log 2$\, $\\sq
rt{2}$\, $\\pi$\, among other « classical » numbers\, behave\, in many r
espects\, like almost all real numbers. For instance\, they are expected t
o be normal to base 10\, that is\, one believes that their decimal expansi
on contains every finite block of digits from $\\{0\, \\ldots \, 9\\}$. We
are very far away from establishing such a strong assertion. However\, th
ere has been some small recent progress in that direction. After surveying
classical results and problems on normal numbers\, we will adopt a point
of view from combinatorics on words and show that the decimal expansions o
f $e$\, of any irrational algebraic number\, and of $\\log (1 + \\frac{1}{
a})$\, for a sufficiently large integer $a$\, cannot be `too simple'\, in
a suitable sense.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.p
y?confId=7645
LOCATION: AG69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7645
END:VEVENT
BEGIN:VEVENT
SUMMARY:A brief survey of problems on complete intersections
DTSTART;VALUE=DATE-TIME:20200305T103000Z
DTEND;VALUE=DATE-TIME:20200305T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7695@cern.ch
DESCRIPTION:Abstract: I will discuss some of the problems on complete inte
rsections with primary focus on work done by several people in TIFR.\n\nht
tps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7695
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7695
END:VEVENT
BEGIN:VEVENT
SUMMARY:Commuting Probability and Simultaneous Conjugacy
DTSTART;VALUE=DATE-TIME:20200312T063000Z
DTEND;VALUE=DATE-TIME:20200312T073000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7702@cern.ch
DESCRIPTION:Abstract: In this colloquium I will look at the topic of commu
ting\nprobability in a group\, and that of simultaneous conjugacy of commu
ting\ntuples of elements of a group\, and the relation between the two top
ics. I\nwill give a brief survey of the work done the topic of commuting\n
probabilities\, and give an overview of my work on simultaneous conjugacy.
\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7702
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7702
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ampleness of vector bundles
DTSTART;VALUE=DATE-TIME:20200319T103000Z
DTEND;VALUE=DATE-TIME:20200319T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7719@cern.ch
DESCRIPTION:Abstract : A line bundle L on a smooth projective variety X i
s called\nample if some positive multiple mL of L gives a closed embedding
of X into\na projective space. A vector bundle V on X is called ample if
the\ntautological line bundle on the associated projective bundle P(E) ove
r X\nis ample. In this talk\, we will discuss about the ampleness criterio
n of\nvector bundles on smooth projective varieties.\n\nhttps://indico.tif
r.res.in/indico/conferenceDisplay.py?confId=7719
LOCATION: AG69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7719
END:VEVENT
BEGIN:VEVENT
SUMMARY:K\\"ahler Geometry of Moduli of Representations of Quivers
DTSTART;VALUE=DATE-TIME:20201015T103000Z
DTEND;VALUE=DATE-TIME:20201015T123000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7826@cern.ch
DESCRIPTION:Abstract:\n\nIn this talk\, I shall discuss some holomorphic a
spects of moduli spaces of\nfinite dimensional\nsemistable representations
of a finite quiver. Namely\, I shall describe\nthe construction\nof a nat
ural Hermitian holomorphic line bundle on the stratified moduli\nspace of
semistable\nrepresentations\, and show that the curvature of this line bun
dle on each\nstratum of the\nmoduli space is a scalar multiple of the K\\"
ahler form of that stratum. I\nshall then recall\nthe definition of the te
nsor product $Q \\otimes Q'$ of two quivers $Q$ and\n$Q'$\, and define the
tensor\nproduct $V \\otimes W$ of a representation $V$ of $Q$ with a repr
esentation\n$W$ of $Q'$\, and discuss\nthe semistability of $V \\otimes W$
. Moreover\, I shall describe a relation\nbetween the natural line\nbundle
s on the moduli spaces of representations of $Q\, Q'$ and $Q \\otimes\nQ'$
.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7826
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7826
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Inertia Conjecture and Its Generalizations
DTSTART;VALUE=DATE-TIME:20201022T103000Z
DTEND;VALUE=DATE-TIME:20201022T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7832@cern.ch
DESCRIPTION:Abstract:\n\nIn this talk\, I will present Abhyankar's Inertia
Conjecture\, some of its\ngeneralizations and evidence towards these prob
lems.\n\nIn 1957\, Abhyankar conjectured that the finite groups that occur
as the\nGalois groups of the \\'{e}tale connected Galois covers of the af
fine line\nover an algebraically closed field of prime characteristic $p$
are\nprecisely the quasi $p$-groups (groups generated by their Sylow\n$p$-
subgroups). This is now a Theorem due to Serre and Raynaud. In 2001\,\nAbh
yankar proposed a refined conjecture on the inertia groups that occur\nove
r $\\infty$ for such covers\, now known as the Inertia Conjecture. The\nco
njecture remains wide open at the moment. We will see the previously\nknow
n evidence and discuss the new ones together with the technique used.\nWe
will also see some generalizations of the conjecture and the evidence\ntow
ards them. The talk will be based on the articles `On the Inertia\nConject
ure for alternating group covers'\, J. Pure Appl. Agebra\, vol. 224\,\n9\,
2020. https://doi.org/10.1016/j.jpaa.2020.106363. (with Manish Kumar)\nan
d `The Inertia Conjecture and its generalizations'\, Preprint\, 2020.\narX
iv:2002.04934(Submitted).\n\nhttps://indico.tifr.res.in/indico/conferenceD
isplay.py?confId=7832
LOCATION: over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7832
END:VEVENT
BEGIN:VEVENT
SUMMARY:Torsion groups of Mordell curves over number fields.
DTSTART;VALUE=DATE-TIME:20201029T103000Z
DTEND;VALUE=DATE-TIME:20201029T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7846@cern.ch
DESCRIPTION:Abstract: Computing the torsion groups of elliptic curves defi
ned over number fields is a classical topic and it has a vast literature i
n algebraic number theory. Any elliptic curve of the form $y^2 = x^3 + c$
is called Mordell curve. We know that the Mordell curve is a well-studied
curve in the\nfamily of CM-elliptic curves. \n\nIn this talk\, we will dis
cuss the classification of torsion groups of rational Mordell Curves expli
citly over cubic fields as well as over sextic fields. Also\, we present t
he classification of torsion groups of Mordell Curves over cubic fields.
For Mordell curves over sextic fields\, we provide all possible torsion gr
oups. \n\nIn the second part\, we discuss torsion group of Mordell curves
over higher degree number fields using some techniques of Galois represent
ations.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7
846
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7846
END:VEVENT
BEGIN:VEVENT
SUMMARY:Relative holomorphic connections and moduli space of logarithmic c
onnections singular over a finite subset of a compact Riemann surface.
DTSTART;VALUE=DATE-TIME:20201105T103000Z
DTEND;VALUE=DATE-TIME:20201105T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7845@cern.ch
DESCRIPTION:Abstract : In this talk we discuss two problems. It is firstly
about\nthe relative holomorphic connections and we give a sufficient cond
ition\nfor the existence of relative holomorphic connections in a vector b
undle\nover a complex analytic family of compact connected complex manifol
ds.\nwe show that the relative Chern classes of a holomorphic vector bundl
e\nover a family of compact and K\\"ahler manifolds vanish if the bundle\
nadmits a relative holomorphic connection.\n\nSecondly\, we give a descrip
tion of certain invariants of the moduli space\nof logarithmic connections
singular over a finite subset of a compact\nRiemann surface with fixed re
sidues. This moduli space is known to be\nquasi-projective variety. We com
pute the Picard group of the moduli space\nand show that the moduli space
does not admit any non-constant algebraic\nfunctions\, although it admits
non-constant holomorphic functions.\n\nhttps://indico.tifr.res.in/indico/c
onferenceDisplay.py?confId=7845
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7845
END:VEVENT
BEGIN:VEVENT
SUMMARY:Representation theory without vector spaces
DTSTART;VALUE=DATE-TIME:20201126T113000Z
DTEND;VALUE=DATE-TIME:20201126T123000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7861@cern.ch
DESCRIPTION:Abstract: A modern view of representation theory is that it is
a study not just of individual representations (say\, finite dimensional
representations of an affine (super)group scheme G over an algebraically c
losed field k) but also of the category Rep(G) formed by them. The propert
ies of Rep(G) can be summarized by saying that it is a symmetric tensor ca
tegory (shortly\, STC) which uniquely determines G. It is therefore natura
l to ask: does the study of STC reduce to group representation theory\, or
is it more general? In other words\, do there exist STC other than Rep(G)
? If so\, this would be interesting\, since one can do algebra in any STC\
, and in categories other than Rep(G) this would be a new kind of algebra.
\n\nThe answer turns out to be “yes”\, and beautiful examples in chara
cteristic zero were provided by Deligne-Milne in 1981. These very interest
ing categories are interpolations of representation categories of classica
l groups GL(n)\, O(n)\, Sp(n) to arbitrary values of n in k. Deligne later
generalized them to symmetric groups and also to characteristic p\, where
\, somewhat unexpectedly\, one needs to interpolate n to p-adic integer va
lues rather than elements of k. All these categories violate an obvious ne
cessary condition for a STC to have any realization by finite dimensional
vector spaces (and in particular to be of the form Rep(G)): for each objec
t X the length of the n-th tensor power of X grows at most exponentially w
ith n. We call this property “moderate growth”. So it is natural to as
k if there exist STC of moderate growth other than Rep(G).\n\nA remarkable
theorem of Deligne (2002) says that in characteristic zero\, the answer i
s “no”: any such category is of the form Rep(G)\, where G is an affine
supergroup scheme\; in other words\, it can be realized in supervector sp
aces. In particular\, algebra in these categories is just the usual one wi
th equivariance under some supergroup G.\n\nHowever\, in characteristic p
the situation is much more interesting. Namely\, Deligne’s theorem is kn
own to fail in any characteristic p>0. The simplest exotic symmetric tenso
r category of moderate growth (i.e.\, not of the form Rep(G)) for p>3 is t
he semisimplification of the category of representations of Z/p\, called t
he Verlinde category. For example\, for p=5\, this category has an object
X such that X^2=X+1\, so X cannot be realized by a vector space (as its di
mension would have to be the golden ratio or its conjugate). I will discus
s some aspects of algebra in these categories\, in particular failure of P
BW theorem for Lie algebras (and how to fix it) and Ostrik’s generalizat
ion of Deligne’s theorem in characteristic p. I will also discuss new ST
C in characteristic p constructed in my joint work with Dave Benson and Vi
ctor Ostrik. There is a hope that any STC of moderate growth in characteri
stic p is the representation category of an affine group scheme in one of
them.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=786
1
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7861
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Hilbert scheme of points on affine space.
DTSTART;VALUE=DATE-TIME:20201202T043000Z
DTEND;VALUE=DATE-TIME:20201202T053000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7876@cern.ch
DESCRIPTION:Abstract: I will discuss the Hilbert scheme of d points in aff
ine n-space\, with some examples. This space has many irreducible componen
ts for n at least 3 and has been poorly understood. For n greater than d\,
we determine the homotopy type of the Hilbert scheme in a range of dimens
ions. Many questions remain. (Joint with Marc Hoyois\, Joachim Jelisiejew\
, Denis Nardin\, Maria Yakerson.)\n\nhttps://indico.tifr.res.in/indico/con
ferenceDisplay.py?confId=7876
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7876
END:VEVENT
BEGIN:VEVENT
SUMMARY:The stable Adams conjecture
DTSTART;VALUE=DATE-TIME:20201210T103000Z
DTEND;VALUE=DATE-TIME:20201210T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7891@cern.ch
DESCRIPTION:Abstract: The Adams conjecture\, perhaps one of the most celeb
rated results\n\nin the subject of stable homotopy theory\, was resolved b
y Quillen and\nSullivan independently in the 1970s. Essentially\, the Ada
ms conjecture\nsays that the q-th Adams operation on topological K-theory
composed with\nthe J-homomorphism can be deformed continuously to the J-ho
momorphism\nitself if localized away from q. The stable enhancement of the
Adams\nconjecture (which is only possible in the complex case) claims tha
t this\ndeformation can be achieved within the space of infinite loop maps
from BU\nto the classifying space of spherical bundles. We recently found
that the\nonly accepted proof of the stable Adams conjecture\, which is d
ue to\nFriedlander (1980)\, has a mistake. In this talk\, I will explain t
he\nmistake\, reformulate the statement of the stable Adams conjecture\, s
ketch\nour new proof of the stable Adams conjecture and discuss some of th
e\nramifications. This is a work joint with N. Kitchloo.\n\nhttps://indico
.tifr.res.in/indico/conferenceDisplay.py?confId=7891
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7891
END:VEVENT
BEGIN:VEVENT
SUMMARY:Finiteness theorems on algebraic groups with good reduction.
DTSTART;VALUE=DATE-TIME:20210114T053000Z
DTEND;VALUE=DATE-TIME:20210114T063000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7912@cern.ch
DESCRIPTION:Abstract: The analysis of linear algebraic groups with good re
duction can\nbe traced back to the work of G.Harder and B.H.Gross where th
e focus was\nover number fields. In this talk\, I will discuss some recent
progress in\nthis direction over more general fields and sketch the ideas
behind the\nproof of a finiteness theorem on special unitary groups of qu
aternionic\nskew-hermitian forms with good reduction. I will also state so
me related\nconjectures and open problems.\n\nhttps://indico.tifr.res.in/i
ndico/conferenceDisplay.py?confId=7912
LOCATION: via zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7912
END:VEVENT
BEGIN:VEVENT
SUMMARY:Derived deformation rings and adjoint Selmer groups for GL_N over
a CM field
DTSTART;VALUE=DATE-TIME:20210121T103000Z
DTEND;VALUE=DATE-TIME:20210121T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7991@cern.ch
DESCRIPTION:Given a cuspidal automorphic representation $pi$ on $GL_N(F)$\
, for a CM field $F$ with Galois representation $rho_pi$\, say\, ordinary
at $p$\, we define and study\, under certain assumptions\, a homomorphism
from the fundamental group of the deformation of $rho_pi$ to its dual adjo
int Selmer group. It has been defined and studied earlier by Galatius and
Venkatesh under stricter assumptions. Our more general setting shows a new
feature of this homomorphism\, namely the relation between the derived de
formation ring of $rho_pi$ and the Bloch-Kato conjecture for the adjoint r
epresentation of $rho_pi$. We treat as well the situation of Hida families
. This is a joint work with E. Urban.\n\nhttps://indico.tifr.res.in/indico
/conferenceDisplay.py?confId=7991
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7991
END:VEVENT
BEGIN:VEVENT
SUMMARY:Structure of finite free resolutions
DTSTART;VALUE=DATE-TIME:20210204T103000Z
DTEND;VALUE=DATE-TIME:20210204T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7931@cern.ch
DESCRIPTION:Abstract: Codimension $2$ Cohen Macaulay varieties (respective
ly codimension $3$ Gorenstein varieties) come from rank condition on $n\\t
imes (n+1)$ matrices (respectively a skew symmetric matrix). Weyman relate
d problem of codimension $3$ varieties with the classification of semi-sim
ple Lie algebra. In the first part of the talk\, for Dynkin type $E_6$\, w
e define an interesting family of perfect ideals of codimension $3$\, with
$5$ generators\, of Cohen Macaulay type $2$ with the trivial multiplicati
on on Tor algebra. In the second part of the talk\, we explore spinor stru
cture on free resolutions of codimension $4$ Gorenstein ideals. For such i
deals with $4$\, $6$\, $7$\, $8$ and $9$ generators\, we present the minim
al number of generators of ideals among spinor coordinates.\n\nhttps://ind
ico.tifr.res.in/indico/conferenceDisplay.py?confId=7931
LOCATION: Over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7931
END:VEVENT
BEGIN:VEVENT
SUMMARY:Intrinsic diophantine approximation on $S^3$ and sums of Kloosterm
an sums
DTSTART;VALUE=DATE-TIME:20210211T103000Z
DTEND;VALUE=DATE-TIME:20210211T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7951@cern.ch
DESCRIPTION:Abstract: Let $S^3$ denote the unit sphere in $\\mathbb{R}^4$.
In a letter\nabout the efficiency of a universal set of quantum gates\, S
arnak raised\nthe question of how well one can approximate points on $S^3$
by rational\npoints of small height. In particular\, given $r \\in \\math
bb{N}$\, how large\ndoes $\\epsilon$ need to be so that any point on $S^3$
can be approximated\nwithin $\\epsilon$ to a point of the form $\\mathbf{
x}/r$\, with $\\mathbf{x}\n\\in \\mathbb{Z}^4$? Using the smooth $\\delta$
-function form of the\nHardy-Littlewood circle method\, Nasser Sardari sho
wed that $\\epsilon \\gg\nr^{-1/3+o(1)}$ is sufficient. In this talk\, I w
ill describe how a variant\nof the Linnik conjecture\, which concerns sums
of Kloosterman sums\, allows\nus to take a smaller value of $\\epsilon$.
Joint work with Tim Browning and\nRaphael Steiner.\n\nhttps://indico.tifr.
res.in/indico/conferenceDisplay.py?confId=7951
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7951
END:VEVENT
BEGIN:VEVENT
SUMMARY:Algebraic K-theory of stacks
DTSTART;VALUE=DATE-TIME:20210218T103000Z
DTEND;VALUE=DATE-TIME:20210218T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7952@cern.ch
DESCRIPTION:Abstract: In the study of moduli problems and equivariant geom
etry of\nschemes with group actions\, one is naturally led to consider cer
tain\ngeometric spaces called algebraic stacks. We can understand these sp
aces\nby studying various cohomological invariants of these geometric obje
cts\nsuch as algebraic K-theory. In this talk\, we start by giving an\nint
roduction to the algebraic K-theory of stacks. After recalling some\nbasic
properties\, we will explain Weibel's conjecture for stacks. This\nconcer
ns the vanishing of certain negative K-groups and was proven in\njoint wor
k with Tom Bachmann\, Adeel Khan and Vladimir Sosnilo.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=7952
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7952
END:VEVENT
BEGIN:VEVENT
SUMMARY:Prescribing Ricci curvature on a product of spheres
DTSTART;VALUE=DATE-TIME:20210225T103000Z
DTEND;VALUE=DATE-TIME:20210225T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7990@cern.ch
DESCRIPTION:Abstract: The Ricci curvature Ric(g) is a symmetric 2-tensor o
n a\nRiemannian manifold (M\,g) that encodes curvature information. The Ri
cci\ncurvature features in several interesting geometric PDEs such as the
Ricci\nflow and the Einstein equation. The nature of Ric(g) as a different
ial\noperator in particular its nonlinearity and the fact that it is degen
erate\nmake these PDEs particularly challenging. In this talk I will addre
ss the\nfollowing question. Given a symmetric 2-tensor T on a manifold M\,
does\nthere exist a metric g such that Ric(g) = T? I will discuss some cl
assical\nresults as well as some recent work in the presence of symmetry.\
n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7990
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7990
END:VEVENT
BEGIN:VEVENT
SUMMARY:Level-sets of correlated Gaussian processes: connectivity and loca
l geometry
DTSTART;VALUE=DATE-TIME:20210318T103000Z
DTEND;VALUE=DATE-TIME:20210318T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7989@cern.ch
DESCRIPTION:Abstract: In this talk we will review some recent developments
in the\nstudy of percolation of Gaussian free field level-sets on the hyp
ercubic\nlattice in three and more dimensions. As a canonical percolation
model\nwith slow algebraic decay of correlations\, the new methodologies t
hat\nemerged in the course of these developments form a robust toolkit for
\nanswering some classical questions in percolation theory in non-classica
l\ncontexts. We will spend considerable time discussing the motivation beh
ind\nthis model\, in particular its interplay with other very natural ques
tions\nin Probability theory as well the rich interplay with the potential
theory\nof random walks which is its another appealing feature. The main
focus of\nthe talk will be a recent result on equality of several natural
critical\nparameters associated with this model --- relevant for understan
ding the\nlocal geometry of level-set components. No prior knowledge of p
ercolation\ntheory is necessary. Based on joint work with H. Duminil-Copin
\, Pierre-F\nRodriguez and Franco Severo.\n\nhttps://indico.tifr.res.in/in
dico/conferenceDisplay.py?confId=7989
LOCATION: Over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7989
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the distribution of S-integral lattice points under isotropic q
uadratic forms
DTSTART;VALUE=DATE-TIME:20210325T103000Z
DTEND;VALUE=DATE-TIME:20210325T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-7988@cern.ch
DESCRIPTION:Abstract: The Oppenheim conjecture and related problems are on
e of the\nhistorical topics in homogeneous dynamics and its application to
number\ntheory. In this talk\, I briefly review which kind of problems ar
e studied\nin this area and talk about their generalization to the S-arith
metic\nspace.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?co
nfId=7988
LOCATION: over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=7988
END:VEVENT
BEGIN:VEVENT
SUMMARY:Combining Rational maps and Kleinian groups via orbit equivalence
DTSTART;VALUE=DATE-TIME:20210415T103000Z
DTEND;VALUE=DATE-TIME:20210415T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8010@cern.ch
DESCRIPTION:Abstract: We develop a new orbit equivalence framework for hol
omorphically\ncombining the dynamics of complex polynomials with that of K
leinian\nsurface groups. We show that the only torsion-free Fuchsian group
s that\ncan be thus combined are punctured sphere groups. We describe a ne
w class\nof maps that are topologically orbit-equivalent to Fuchsian punct
ured\nsphere groups. We call these higher Bowen-Series maps. The existence
of\nthis class ensures that\, unlike in higher dimensions\, topological o
rbit\nequivalence rigidity fails for Fuchsian groups acting on the circle.
We\nalso classify the collection of Kleinian Bers' boundary groups that a
re\ncombinable in our framework. This is joint work with Sabyasachi Mukher
jee.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8010
LOCATION: via zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8010
END:VEVENT
BEGIN:VEVENT
SUMMARY:Frobenius Algebras and WDVV equations
DTSTART;VALUE=DATE-TIME:20210520T113000Z
DTEND;VALUE=DATE-TIME:20210520T123000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8053@cern.ch
DESCRIPTION:Abstract: I will discuss Frobenius algebras and their connecti
ons to topological quantum field theories and the Witten-Dijkgraff-Verlind
e-Verlinde associativity equations.\n\nhttps://indico.tifr.res.in/indico/c
onferenceDisplay.py?confId=8053
LOCATION: Over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8053
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bezout’s Theorem for plane curves.
DTSTART;VALUE=DATE-TIME:20210524T113000Z
DTEND;VALUE=DATE-TIME:20210524T123000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8055@cern.ch
DESCRIPTION:Abstract: In this talk I will discuss about the intersection n
umber\nbetween to plane curves and its relation to the degree of the curve
s. The\nBezut’s theorem is a fundamental theorem in this context which s
ays that\ntwo plane curves of degree d and d’ intersects at dd’ points
.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8055
LOCATION: over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8055
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quadratic forms and their invariants
DTSTART;VALUE=DATE-TIME:20210528T113000Z
DTEND;VALUE=DATE-TIME:20210528T123000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8057@cern.ch
DESCRIPTION:Abstract: We will discuss the following basic question: how ca
n one determine if two quadratic forms with coefficients in a field are eq
uivalent? In order to study this question\, quadratic forms are often stud
ied using their invariants living in suitable groups. Time permitting\, w
e will describe some deep results about the classification of quadratic fo
rms proved in the last 20-25 years and discuss some examples.\n\nhttps://i
ndico.tifr.res.in/indico/conferenceDisplay.py?confId=8057
LOCATION: Over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8057
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Springer Correspondence
DTSTART;VALUE=DATE-TIME:20210531T113000Z
DTEND;VALUE=DATE-TIME:20210531T123000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8058@cern.ch
DESCRIPTION:Abstract: Using the Jordan canonical form\, the number of conj
ugacy classes of nilpotent n x n matrices can be seen to be equal to the n
umber of irreducible representations of the permutation group S_n. In this
talk\, I will give an introduction to the Springer correspondence which p
rovides a deeper geometric understanding of the above numerical coincidenc
e.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8058
LOCATION: Over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8058
END:VEVENT
BEGIN:VEVENT
SUMMARY:The Erdos-Kac theorem: an introduction to probabilistic number the
ory
DTSTART;VALUE=DATE-TIME:20210604T113000Z
DTEND;VALUE=DATE-TIME:20210604T123000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8066@cern.ch
DESCRIPTION:Abstract: A famous result of Hardy and Ramanujan states that a
lmost every\nlarge integer $N$ has approximately $\\log \\log N$ prime fac
tors. This\nresult was subsequently refined by Erdos and Kac\, who proved
that the\ndistribution of the number of prime factors of an integer\, when
suitably\nnormalised\, may be modelled by the Gaussian random variable. I
n this talk\,\nI will discuss some motivations of the Erdos-Kac theorem an
d outline its\nproof.\n\nhttps://indico.tifr.res.in/indico/conferenceDispl
ay.py?confId=8066
LOCATION: Over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8066
END:VEVENT
BEGIN:VEVENT
SUMMARY:From buildings to factor complex
DTSTART;VALUE=DATE-TIME:20210715T103000Z
DTEND;VALUE=DATE-TIME:20210715T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8108@cern.ch
DESCRIPTION:ABSTRACT: We will consider three families of groups - arithmet
ic groups\, mapping class groups and groups of outer automorphisms of a fr
ee group. The study of arithmetic groups has had a profound influence on h
ow we understand the latter two classes of groups. In this talk\, we will
specifically draw parallels between the associated simplicial complexes -
Tits building\, curve complex and free factor complex - from a topological
point of view.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?
confId=8108
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8108
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mixed characteristic birational algebraic geometry
DTSTART;VALUE=DATE-TIME:20210826T043000Z
DTEND;VALUE=DATE-TIME:20210826T053000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8136@cern.ch
DESCRIPTION:Abstract: Recently\, Bhargav Bhatt has proved a vanishing theo
rem for sheaf\ncohomology on certain non-Noetherian schemes. I will expla
in\nhow this vanishing theorem is related to various classical vanishing\n
results in characteristic zero and p. I will then discuss how we can use\
nthis to prove geometric results in birational algebraic geometry in mixed
\ncharacteristic. This is joint work with Bhatt\, Ma\, Patakfalvi\, Tucker
\,\nWaldron and Witaszek.\n\nhttps://indico.tifr.res.in/indico/conferenceD
isplay.py?confId=8136
LOCATION: over zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8136
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quasi-metric antipodal spaces and maximal Gromov hyperbolic spaces
.
DTSTART;VALUE=DATE-TIME:20211028T113000Z
DTEND;VALUE=DATE-TIME:20211028T123000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8208@cern.ch
DESCRIPTION:Abstract: A quasi-metric antipodal space $(Z\, \\rho_0)$ is a
compact space $Z$ with a continuous quasi-metric $\\rho_0$ which is of dia
meter one\, and which\nis antipodal\, i.e. for any $\\xi \\in Z$ there exi
sts $\\eta \\in Z$ such that $\\rho_0(\\xi\, \\eta) = 1$. The quasi-metric
$\\rho_0$ defines a positive cross-ratio\nfunction on the space of quadru
ples of distinct points in $Z$\, and a homeomorphism between quasi-metric\
nantipodal spaces is said to be Moebius if it preserves cross-ratios.\n\nA
proper\, geodesically complete Gromov hyperbolic space $X$ is said to be
boundary continuous if the Gromov inner product\nextends continuously to t
he boundary. Then the boundary $\\partial X$ equipped with a visual quasi-
metric is a quasi-metric antipodal space.\nThe space $X$ is said to be max
imal if for any proper\, geodesically complete\, boundary continuous\nGrom
ov hyperbolic space $Y$\, if there is a Moebius homeomorphism $f : \\parti
al Y \\to \\partial X$\,\nthen $f$ extends to an isometric embedding $F :
Y \\to X$. We call such spaces maximal Gromov hyperbolic spaces.\n\nWe giv
e an explicit description of all maximal Gromov hyperbolic spaces\, in par
ticular showing that they are contractible. \nWe show that any proper\, ge
odesically complete\, boundary continuous Gromov hyperbolic space embeds\n
isometrically into a maximal Gromov hyperbolic space which is unique up to
isometry\, and the image of the embedding is cobounded.\nWe prove an equi
valence of categories between quasi-metric antipodal spaces and maximal Gr
omov hyperbolic spaces\, namely: any quasi-metric antipodal\nspace is Moeb
ius homeomorphic to the boundary of a maximal Gromov hyperbolic space\, an
d any Moebius\nhomeomorphism $f : \\partial X \\to \\partial Y$ between bo
undaries of maximal Gromov hyperbolic spaces $X\, Y$\nextends to a surject
ive isometry $F : X \\to Y$. This is part of a more general\nequivalence b
etween certain compact spaces called antipodal spaces and their associated
metric spaces called Moebius spaces.\n\nhttps://indico.tifr.res.in/indico
/conferenceDisplay.py?confId=8208
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8208
END:VEVENT
BEGIN:VEVENT
SUMMARY:New results on Cofibrants and Gorenstein projectives and applicati
ons.
DTSTART;VALUE=DATE-TIME:20211118T103000Z
DTEND;VALUE=DATE-TIME:20211118T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8223@cern.ch
DESCRIPTION:Abstract: We will talk about a conjectured relation between "c
ofibrant"\nmodules and Gorenstein projective modules for arbitrary groups
over any\ncommutative ring of finite global dimension. We will first expla
in what\nthese classes of modules are and then report on my new work that
proves\nthis conjecture for a large class of groups. If time permits\, we
will then\nshow how the behaviour of these classes of modules with respect
to each\nother has far-reaching applications in generating stable module\
ncategories.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?con
fId=8223
LOCATION: AG66 as well as Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8223
END:VEVENT
BEGIN:VEVENT
SUMMARY:Castelnuovo-Mumford Regularity of Quadratic Sequences with applica
tions to Binomial Ideals
DTSTART;VALUE=DATE-TIME:20211125T103000Z
DTEND;VALUE=DATE-TIME:20211125T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8238@cern.ch
DESCRIPTION:Abstract: Cutkosky-Herzog-Trung and independently Kodiyalam pr
oved that\nthe Castelnuovo-Mumford regularity of powers of homogeneous ide
als in a\npolynomial ring is bounded above by a linear function. Given a h
omogeneous\nideal\, finding this linear function is a very difficult task.
In this\ntalk\, we will compute the linear function for the ideals genera
ted by\nhomogeneous quadratic sequences. For this\, we will start with the
\ndefinition of d-sequence and its generalization to the quadratic sequenc
e.\nWe then talk about the regularity upper bound of powers of an ideal\ng
enerated by a quadratic sequence in terms of its related ideals and\ndegre
es of generators. We then apply these results to the binomial edge\nideals
for several computations.\n\nhttps://indico.tifr.res.in/indico/conference
Display.py?confId=8238
LOCATION: AG 66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8238
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gauss sums
DTSTART;VALUE=DATE-TIME:20211202T103000Z
DTEND;VALUE=DATE-TIME:20211202T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8241@cern.ch
DESCRIPTION:Abstract: Classical Gauss sums appear in many number theoretic
\ncontexts. `Non-abelian' Gauss sums can be defined attached to finite \n
dimensional representations of the general linear group in n variables \no
ver a finite field. \n\nWe will try to present some aspects of these Gauss
sums.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=82
41
LOCATION: (AG-69) as well as Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8241
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some results and conjectures in the theory of vertex operator alge
bras
DTSTART;VALUE=DATE-TIME:20211209T053000Z
DTEND;VALUE=DATE-TIME:20211209T063000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8247@cern.ch
DESCRIPTION:Abstract: Individual vertex operators arose in the mathematica
l literature\nnearly four decades ago in Lepowsky-Wilson's Lie algebraic p
roof of the \nRogers-Ramanujan identities. Vertex operator algebras (VOAs)
were also \ncentral to Borcherds' proof of the moonshine conjecture -- th
e moonshine \nmodule constructed by Frenkel-Lepowsky-Meurman and used in\n
Borcherds' proof is a VOA. Since their inception\, the study of VOAs has\
nseen a rapid growth guided by various conjectures in mathematics and\nph
ysics.\n\nMost well-known VOAs are in some way connected to affine Lie alg
ebras and\ntheir study is naturally related to representation theory\, te
nsor \ncategories\, algebraic combinatorics and number theory.\n\nIn this
talk\, I will survey a selection of results and conjectures\npertaining to
these topics. I will focus on (a subset of) --\n1. Rogers-Ramanujan-type
identities related to affine Lie algebras\,\n2. Tensor categorical aspects
related to conformal embeddings of VOAs\,\n3. Some problems in the repres
entation theory of twisted affine Lie\nalgebras at non-integrable levels.\
n\nParts of the talk will be based on joint works with my collaborators.\n
\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8247
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8247
END:VEVENT
BEGIN:VEVENT
SUMMARY:The negative Pell conjecture and related problems: reciprocity law
s in higher nilpotency class
DTSTART;VALUE=DATE-TIME:20211217T103000Z
DTEND;VALUE=DATE-TIME:20211217T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8252@cern.ch
DESCRIPTION:Abstract: In this talk I will overview an upcoming joint work
with Peter Koymans\, settling a conjecture made by Nagell (made around 193
0) on the solvability of the negative Pell equation\, in the refined form
proposed by Stevenhagen in 1995. We achieved this by discovering certain r
eciprocity laws for (so-called) governing expansions: such reciprocity law
s can be thought as higher-nilpotency generalizations of a reciprocity law
established by Re'dei around the 30's (which corresponds to nilpotency cl
ass 2). Governing expansions were introduced by Smith in 2017 in his groun
dbreaking work on Goldfeld's and Cohen--Lenstra's conjectures\, where he u
sed them to establish reflection-principles to compare 2-power Selmer grou
ps of different twists of a Galois module: we used these objects in previo
us work to establish a simplicial generalization of Gauss' genus theory fr
om quadratic to multi-quadratic fields\, a result whose proof is based on
the control of the Lie-algebra of certain Galois groups over the rational
numbers. Smith's reflection principles broke down in the study of the nega
tive Pell equation\, and our reciprocity laws provide new supplementary re
flection principles for this problem. A number of seemingly different prob
lems are affected by these same difficulties: ranging from Chowla's conjec
ture over function fields (non-vanishing of L-functions at 1/2 for 100% of
characters)\, open cases of Goldfeld's conjecture\, statistics of Iwasawa
's modules\, to the proof that the Brauer--Manin obstruction is the only o
bstruction to the Hasse principle for Kummer surfaces over number fields (
under finiteness of Tate--Shafarevich groups of abelian surfaces). I will
conclude explaining what we expect to achieve with these new tools on thos
e other problems.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.p
y?confId=8252
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8252
END:VEVENT
BEGIN:VEVENT
SUMMARY:Poincar\\'{e} and Picard bundles for moduli spaces of vector bundl
es over nodalcurves
DTSTART;VALUE=DATE-TIME:20220106T103000Z
DTEND;VALUE=DATE-TIME:20220106T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8263@cern.ch
DESCRIPTION:Abstract: Poincar\\'{e} and Picard bundles and their different
variants have been a topic of interest ever since the quest for moduli sp
aces of vector bundles was initiated\, owing to their universality. Though
a great deal is known about these objects in the case of smooth curves\,
the study on singular curves has been relatively slow. Interestingly\, the
results for irreducible nodal curves are very similar to those for smooth
curves\; however\,the proofs are different and difficult. It was known fo
r a long time that there does not exist a Poincar\\'{e} bundle for the mod
uli problem of vector bundles on smooth curves if the rank and degree are
not coprime. We primarily aim to discuss the non-existence of a Poincar\\'
{e} bundle parametrised by the moduli space of vector bundles on nodal cur
ves when the rank and degree are not coprime. There has also been a consid
erable amount of interest to understand the stability of Poincar\\'{e} and
projective Poincar\\'{e} bundles as well as Picard and projective Picard
bundles.The secondary aim of the talk is to discuss the stability of proje
ctive Poincar\\'{e} and Picardbundles\, again when the degree and rank are
not relatively prime to each other in the context of nodal curves. On the
way to achieve these goals\, we compute the codimension of a few closed s
ubsets of the moduli spaces. They are of independent interest and have oth
er applications\; we discuss a few of them. This is a joint work with Prof
. Usha Bhosle and Dr. Sanjay Singh.\n\nhttps://indico.tifr.res.in/indico/c
onferenceDisplay.py?confId=8263
LOCATION: Maths Seminar Room (A-369) as well as via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8263
END:VEVENT
BEGIN:VEVENT
SUMMARY:Orthogonality of invariant vectors
DTSTART;VALUE=DATE-TIME:20220203T103000Z
DTEND;VALUE=DATE-TIME:20220203T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8285@cern.ch
DESCRIPTION:Abstract: Let $(\\pi\,V)$ be an irreducible complex representa
tion of a\nfinite group $G$ and let $\\langle~\, ~\\rangle_\\pi$ be the st
andard\n$G$-invariant inner product on $\\pi.$ Let $H$ and $K$ be subgroup
s of $G$\nsuch that the space of $H$-invariant vectors as well as the spac
e of\n$K$-invariant vectors of $\\pi$ are one dimensional. Fix an $H$-inva
riant\nunit vector $v_H$ and a $K$-invariant unit vector $v_K.$ Benedict G
ross\ndefines the Correlation constant $c(\\pi\; H\, K)$ of $H$ and $K$ wi
th\nrespect to $\\pi.$ It turn out that $c(\\pi\; H\, K)=|\\langle v_H\,\n
v_K\\rangle_\\pi|^2.$\n\nIn this talk we analyze the Correlation constant
$c(\\pi\; H\, K)\,$ when\n$G={\\rm GL}_2(\\mathbb{F}_q)\,$ where $\\mathbb
{F}_q$ is the finite field\nwith $q=p^f$ elements for some odd prime $p\,$
$H$ (resp. $K$) is the split\n(resp. non split) torus of $G.$ This is joi
nt with U. K. Anandavardhanan.\n\nhttps://indico.tifr.res.in/indico/confer
enceDisplay.py?confId=8285
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8285
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some works of Maryam Mirzakhani (1977-2017)
DTSTART;VALUE=DATE-TIME:20220210T103000Z
DTEND;VALUE=DATE-TIME:20220210T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8294@cern.ch
DESCRIPTION:Abstract: I will present in this lecture some of the works of
Maryam\nMirzakhani. Maryam Mirzakhani was a mathematician working in hyper
bolic\ngeometry\, studying curves on surfaces and more precisely their\ndi
stribution.\n\nRather than giving a precise account of her numerous and am
azing results\,\nI will use one of her work as a thread — or a pretext
— to present some\nbasic ideas of geometry as well as a little history
of the subject: What\nis a surface? What is hyperbolic geometry? How do ma
thematicians count\ncurves on surfaces?\n\nhttps://indico.tifr.res.in/indi
co/conferenceDisplay.py?confId=8294
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8294
END:VEVENT
BEGIN:VEVENT
SUMMARY:On topics in Iwasawa theory and p-adic Langlands program.
DTSTART;VALUE=DATE-TIME:20220217T103000Z
DTEND;VALUE=DATE-TIME:20220217T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8310@cern.ch
DESCRIPTION:Abstract: Recent developments in the p-adic Langlands program
allow us to\nrevisit classical conjectures in Iwasawa Theory which help in
\nunderstanding the arithmetic of Galois representations arising from\nell
iptic curves\, modular forms and automorphic forms.\n\nThis talk will cove
r various aspects of my research domain and will be\nexpository in nature.
We will present results in Iwasawa Theory and p-adic\nHodge Theory and co
mbine them to frame the signed Iwasawa main conjectures\nfor non-ordinary
automorphic representations. Alongside\, we will also\ndiscuss Greenbergâ
€™s p-rationality conjecture and use it to construct\nGalois represent
ations with big open images in reductive groups.\nFurthermore\, we will di
scuss results in p-adic functional analysis and\nshow the existence of rig
id analytic vectors in the crystalline\nrepresentations arising from the p
-adic Langlands program. These works are\na culmination of several project
s with various collaborators.\n\nhttps://indico.tifr.res.in/indico/confere
nceDisplay.py?confId=8310
LOCATION: Over Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8310
END:VEVENT
BEGIN:VEVENT
SUMMARY:Open book decomposition and open book embeddings of closed 3-manif
olds.
DTSTART;VALUE=DATE-TIME:20220224T103000Z
DTEND;VALUE=DATE-TIME:20220224T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8267@cern.ch
DESCRIPTION:Abstract: In the first part\, we will discuss a new proof of t
he existence\nof an open book decomposition for a closed non-orientable 3
–manifold. This\nopen book decomposition is analogous to a planar open b
ook decomposition\nfor a closed orientable 3–manifold. More precisely\,
we give an open book\ndecomposition of a given closed non-orientable 3–
manifold with the pages\npunctured Möbius bands and the monodromy product
of Dehn twists.\n\nIn the second part\, we will discuss open book embeddi
ngs of closed\nnon-orientable 3-manifolds into 5-manifolds.\n\nThis is a j
oint work with Suhas Pandit and A Selvakumar.\n\nhttps://indico.tifr.res.i
n/indico/conferenceDisplay.py?confId=8267
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8267
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some results on Seshadri constants
DTSTART;VALUE=DATE-TIME:20220303T103000Z
DTEND;VALUE=DATE-TIME:20220303T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8320@cern.ch
DESCRIPTION:Abstract: Seshadri constants were defined by Demailly as a loc
al measure\nof positivity of line bundles. He introduced this notion motiv
ated by\nSeshadri's ampleness criterion for line bundles. Later\, Hacon ge
neralized\nthe notion of Seshadri constants to vector bundles. Seshadri co
nstants\nhave now become a central object of study in numerous directions
in\nalgebraic geometry\, particularly in the study of linear series. In\ng
eneral\, Seshadri constants are hard to compute and a lot of research is\n
aimed at finding good estimates.\n\nIn this talk\, we will start with basi
cs on Seshadri constants and discuss\nsome important results and connectio
ns to well known questions. We will\nthen focus on computing Seshadri cons
tants for some torus equivariant\nvector bundles at arbitrary points on pr
ojective spaces and Bott towers of\nheight at most 3. This is based on a j
oint work with Jyoti Dasgupta and\nBivas Khan.\n\nhttps://indico.tifr.res.
in/indico/conferenceDisplay.py?confId=8320
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8320
END:VEVENT
BEGIN:VEVENT
SUMMARY:Some results in 4-dimensional Kähler MMP.
DTSTART;VALUE=DATE-TIME:20220317T103000Z
DTEND;VALUE=DATE-TIME:20220317T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8336@cern.ch
DESCRIPTION:Abstract: Given two projective varieties X and Y\, we say that
they are\nbimeromorphic to each other if they have isomorphic non-empty Z
ariski open\nsubsets\, or equivalently\, their function fields are isomorp
hic as\nk-algebras\, where k is the ground field of the varieties X and Y.
This\ndefines an equivalence relation (in the varieties of fixed dimensio
n). The\nMinimal Model Program (MMP) or Mori Program is a tool which aims
to find a\n`good’ and `minimal’ representative in each of these equiva
lence classes.\nIn this talk I will present some new results in Kähler MM
P for\n4-dimensional Kähler varieties. This is a joint work with Christop
her\nHacon and Mihai Paun.\n\nhttps://indico.tifr.res.in/indico/conference
Display.py?confId=8336
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8336
END:VEVENT
BEGIN:VEVENT
SUMMARY:Property (T) versus aTmenability
DTSTART;VALUE=DATE-TIME:20220324T103000Z
DTEND;VALUE=DATE-TIME:20220324T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8343@cern.ch
DESCRIPTION:Abstract: A group has property (T) if its trivial representati
on is\nisolated in the unitary dual. This is equivalent to saying that any
action\nby affine isometries on a Hilbert space has a fixed point. A grou
p is\ncalled aTmenable if it admits a proper action on a Hilbert space. We
shall\nreview those properties and see what happens when we replace the H
ilbert\nspace by an ell^p space.\n\nhttps://indico.tifr.res.in/indico/conf
erenceDisplay.py?confId=8343
LOCATION: Lecture Room (AG-69) Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8343
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quadratic forms in 8 prime variables
DTSTART;VALUE=DATE-TIME:20220505T103000Z
DTEND;VALUE=DATE-TIME:20220505T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8394@cern.ch
DESCRIPTION:Abstract: I will discuss a recent paper of mine\, the aim of w
hich is to\ncount the number of prime solutions to Q(p_1\,..\,p_8) = N\, f
or a fixed\nquadratic form Q and varying N. The traditional approach to pr
oblems of\nthis type\, the Hardy-Littlewood circle method\, does not quite
suffice. The\nmain new idea is to involve the Weil representation of the
symplectic\ngroups Sp_8(Z/qZ). I will explain what this is\, and what it h
as to do with\nthe original problem. I hope to make the talk accessible to
a fairly\ngeneral audience.\n\nhttps://indico.tifr.res.in/indico/conferen
ceDisplay.py?confId=8394
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8394
END:VEVENT
BEGIN:VEVENT
SUMMARY:On some applications of the notion of Infinity to the study of Alg
ebraic Curves.
DTSTART;VALUE=DATE-TIME:20220616T103000Z
DTEND;VALUE=DATE-TIME:20220616T120000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8449@cern.ch
DESCRIPTION:Abstract:\nThe notion of points at infinity will be used to ex
plain some examples of\nDiophantus\, who found a method of finding rationa
l points on certain\nAlgebraic curves. This notion is used also to explain
the definition of\nthe group law on an Elliptic curve.\n\nhttps://indico.
tifr.res.in/indico/conferenceDisplay.py?confId=8449
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8449
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dirichlet's theorem on primes in arithmetic progressions.
DTSTART;VALUE=DATE-TIME:20220623T103000Z
DTEND;VALUE=DATE-TIME:20220623T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8460@cern.ch
DESCRIPTION:Abstract: Dirichlet proved that there are infinitely many prim
es in an\narithmetic progression of positive integers with no common facto
r. The\nproof is a mixture of analysis and algebra\, and will depend on an
alytic\nproperties of "Dirichlet L-Functions". We will first look at sev
eral\nexamples and then see how to extend the proof to the general case.\n
\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8460
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8460
END:VEVENT
BEGIN:VEVENT
SUMMARY:Times 2\, Times 3 and all that
DTSTART;VALUE=DATE-TIME:20220630T103000Z
DTEND;VALUE=DATE-TIME:20220630T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8471@cern.ch
DESCRIPTION:Abstract: I will provide a gentle introduction to ergodic theo
ry by\ndiscussing the dynamics of some seemingly simple maps.\n\nhttps://i
ndico.tifr.res.in/indico/conferenceDisplay.py?confId=8471
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8471
END:VEVENT
BEGIN:VEVENT
SUMMARY:Well\, Papa\, Can you multiply triplets?
DTSTART;VALUE=DATE-TIME:20220707T103000Z
DTEND;VALUE=DATE-TIME:20220707T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8483@cern.ch
DESCRIPTION:Abstract: The search for hypercomplex numbers in the 19th cent
ury led to\nthe discovery of quaternions. We will briefly run through the
history\nwhich led to this discovery and its impact on mathematics since t
hen. I\nwill also show some applications and generalizations.\n\nhttps://i
ndico.tifr.res.in/indico/conferenceDisplay.py?confId=8483
LOCATION: Via Zoom
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8483
END:VEVENT
BEGIN:VEVENT
SUMMARY:On the arithmetic of elliptic curves
DTSTART;VALUE=DATE-TIME:20220804T103000Z
DTEND;VALUE=DATE-TIME:20220804T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8501@cern.ch
DESCRIPTION:Abstract: The talk will give an introduction to the arithmetic
of elliptic\ncurves defined over rational numbers\, especially the conjec
ture of Birch\nand Swinnerton-Dyer\, and some results.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=8501
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8501
END:VEVENT
BEGIN:VEVENT
SUMMARY:The quantitative distribution of Hecke eigenvalues of cusp forms:
Sato-Tate\, Lang-Trotter and all that.
DTSTART;VALUE=DATE-TIME:20220811T103000Z
DTEND;VALUE=DATE-TIME:20220811T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8510@cern.ch
DESCRIPTION:Abstract: For holomorphic cusp forms of weight $k$ (even)\, le
vel $q$ one\nknows that the Hecke eigenvalues (unnormalised) are all alge
braic\nintegers belonging to a fixed number field $K$ say. This immediatel
y\nimplies that the number of primes $p$\, $(p \, q )= 1$ such the normal
ised Hecke eigenvalues $\\lambda ( p ) = a ( p ) / p^{ ( k - 1 ) /2 }$ whe
re $k$ is the weight $= \\alpha\, \\alpha \\in [ -2\, 2 ] \, {\\alpha}$ al
gebraic is finite. However the number of the unnormalised $a ( p )$ 's wit
h this property i.e $a ( p ) = \\beta\, \\beta \\in O_K$ fixed could a pri
ori be infinite and is the subject matter of the Lang-Trotter conjecture.
We will try to pose these questions in the case of non-holomorphic Maass c
usp forms.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confI
d=8510
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8510
END:VEVENT
BEGIN:VEVENT
SUMMARY:Supercongruences and Derivatives
DTSTART;VALUE=DATE-TIME:20220826T103000Z
DTEND;VALUE=DATE-TIME:20220826T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8524@cern.ch
DESCRIPTION:Abstract: We will see some interesting connections between\nsu
percongruences and derivatives when we replace integers by polynomials. We
will give some applications to characterizations\nand infinitude of speci
al class of primes. We will also see how some fundamental arithmetic quant
ities have interesting factorizations in terms of special primes.\n\nhttps
://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8524
LOCATION: AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8524
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cohomology of algebraic stacks
DTSTART;VALUE=DATE-TIME:20220901T103000Z
DTEND;VALUE=DATE-TIME:20220901T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8529@cern.ch
DESCRIPTION:Abstract: Motivated by moduli theory\, we will discuss how inv
ariants like cohomology\, K-theory\, and motives can be extended to algebr
aic stacks. We will see how this stacky perspective recovers and enhances
the theories of equivariant cohomology and K-theory.\n\nYouTube live link:
https://youtu.be/ACRKh4eABgk\n\nhttps://indico.tifr.res.in/indico/confere
nceDisplay.py?confId=8529
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8529
END:VEVENT
BEGIN:VEVENT
SUMMARY:A Cautionary Tale
DTSTART;VALUE=DATE-TIME:20220908T103000Z
DTEND;VALUE=DATE-TIME:20220908T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8542@cern.ch
DESCRIPTION:Abstract: Let $A \\subseteq B$ be integral domains and $G$ be
a totally\nordered Abelian group. D. Daigle has formulated certain hypothe
ses on\ndegree function $\\deg : B \\rightarrow G \\cup \\lbrace - \\infty
\\rbrace$ so\nthat it is tame in characteristic zero\, i.e.\, $\\deg(D)$
is defined for all\n$A$-derivations $D: B \\rightarrow B$. This study is i
mportant because each\n$D \\in \\der_k(B)$ for which $\\deg(D)$ is defined
\, we can homogenize the\nderivation which is an important and useful tool
in the study of\n$\\G_a$-action on an algebraic variety.\n\nIn arbitrary
characteristic\, $\\G_a$-action on an affine scheme $\\spec(B)$\ncan be in
terpreted in terms of exponential maps on $B$. In this talk we\nshall disc
uss analogous formulations of hypotheses on the degree function\nso that $
\\deg(\\phi)$ is defined for each $A$-linear exponential map $\\phi$\non $
B$. This talk is based on a joint work with N. Gupta.\n\nhttps://indico.ti
fr.res.in/indico/conferenceDisplay.py?confId=8542
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8542
END:VEVENT
BEGIN:VEVENT
SUMMARY:Smooth torus quotients of Richardson varieties in Grassmannian
DTSTART;VALUE=DATE-TIME:20220915T103000Z
DTEND;VALUE=DATE-TIME:20220915T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8550@cern.ch
DESCRIPTION:Abstract : We will study the GIT quotients of Richardson varie
ties in the\nGrassmannian by a maximal torus. We give a necessary and suff
icient\ncombinatorial condition for which the quotient variety is smooth.
If time\npermits we will discuss the projective normality of torus quotien
ts of\nGrassmannian of planes in the complex n space using standard monomi
al\ntheory. The later is based on a joint work with Kannan and Subrahmanya
m.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8550
LOCATION: A369
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8550
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramified class field theory and its application
DTSTART;VALUE=DATE-TIME:20220922T103000Z
DTEND;VALUE=DATE-TIME:20220922T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8577@cern.ch
DESCRIPTION:Abstract: The main aim of this field is to study the abelianiz
ed etale\nfundamental group of a quasi-projective variety in terms of a\nc
ycle-theoretic group. In this talk\, we shall discuss the ramified class\n
field theory of smooth quasi-projective varieties over finite fields. The\
nmain focus of the talk will be to use this theory to prove the failure of
\nNisnevich descent for the Chow groups with modulus. The talk will be bas
ed\non joint works with Prof. Amalendu Krishna.\n\nhttps://indico.tifr.res
.in/indico/conferenceDisplay.py?confId=8577
LOCATION: AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8577
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modularity of Galois representations\, from Ramanujan to Serre's c
onjecture and beyond
DTSTART;VALUE=DATE-TIME:20221006T103000Z
DTEND;VALUE=DATE-TIME:20221006T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8589@cern.ch
DESCRIPTION:Abstract: Ramanujan made a series of influential conjectures i
n his 1916\npaper ``On some arithmetical functions''\non what is now calle
d the Ramanujan $\\tau$ function. A congruence\nRamanujan observed for $\
\tau(n)$ modulo 691 in the paper led to Serre and\nSwinnerton-Dyer develo
ping a geometric theory of mod $p$ modular forms. It\nwas in the context o
f the theory of mod $p$ modular forms that Serre made\nhis modularity conj
ecture\, which was initially formulated in a letter of\nSerre to Tate in 1
973.\n\nI will describe the path from Ramanujan's work in 1916\, to the\n
formulation of a first version of Serre's conjecture in 1973\, to its\nr
esolution in 2009 by Jean-Pierre Wintenberger and myself. I will also\ntr
y to indicate why this subject is very much alive and\, in spite of all\nt
he progress\, still in its infancy. I will end with some questions about
\ncounting mod p Galois representations\, and the use of Serre’s conjec
ture\nin the`` computational Langlands program’'.\n\n-------------------
-------------------------------------------------\n\nJoin Zoom Meeting\nht
tps://tifr-res-in.zoom.us/j/98154315279\n\nMeeting ID: 981 5431 5279\nPass
code: 100644\n\n----------------------------------------------------------
----------\n\nYouTube live link: https://youtu.be/CY-PsvhOQAs\n\n---------
-----------------------------------------------------------\n\nhttps://ind
ico.tifr.res.in/indico/conferenceDisplay.py?confId=8589
LOCATION: AG-66
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8589
END:VEVENT
BEGIN:VEVENT
SUMMARY:Existence of Cannon-Thurston map
DTSTART;VALUE=DATE-TIME:20221013T103000Z
DTEND;VALUE=DATE-TIME:20221013T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8603@cern.ch
DESCRIPTION:Abstract: Let $G$ be a hyperbolic group and $H$ be a hyperbol
ic subgroup\nof $G$. If the embedding $H\\to G$ extends continuously to a
map between\nthe Gromov compactifications of the groups\, this extension i
s called a\nCannon-Thurston map (CT). While it is known that not every hyp
erbolic\nsubgroup embedding in a hyperbolic group admits CT\, over time th
e\nexistence of CT has been proven in many cases. We will start with a sur
vey\nof these results and move on to the following case where CT exists. L
et\n$1\\to N \\to G \\stackrel{\\pi}{\\to} Q\\to 1$ be a short exact seque
nce of\nnon-elementary hyperbolic groups and $K=\\pi^{-1}(Q_1)$\, where $Q
_1$ is a\nqi-embedded subgroup of $Q$. Then $K$ is hyperbolic and $K\\to G
$ admits\nCT. This is part of joint work with Pranab Sardar.\n\nhttps://in
dico.tifr.res.in/indico/conferenceDisplay.py?confId=8603
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8603
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stretch factors of graph maps and polynomial invariants of free-by
-cyclic groups
DTSTART;VALUE=DATE-TIME:20221020T103000Z
DTEND;VALUE=DATE-TIME:20221020T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8620@cern.ch
DESCRIPTION:Abstract: In this talk we will associate two numbers\, the geo
metric and\nhomological stretch factors\, to a graph map and see under wha
t conditions\nthey are equal. We will then upgrade these notions to free g
roup\nautomorphisms. Finally\, we will cast these numbers in terms of two\
npolynomial invariants\, the Alexander polynomial and McMullen polynomial\
,\nassociated to a free-by-cyclic group and see how these polynomials are\
nrelated to each other.\n\n-----------------------------------------------
--\n\nYouTube live link: https://youtu.be/DJQy9fZ8lro\n\n-----------------
---------------------------------\n\nhttps://indico.tifr.res.in/indico/con
ferenceDisplay.py?confId=8620
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8620
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abundance-type problems for generalised pairs
DTSTART;VALUE=DATE-TIME:20221027T103000Z
DTEND;VALUE=DATE-TIME:20221027T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8626@cern.ch
DESCRIPTION:Abstract: In algebraic geometry\, abundance-type problems are
those that\nrelate numerical properties of a certain Cartier divisor with
properties\nof the associated line bundle (such as global generation or th
e existence\nof nonzero sections). In its most basic form\, the abundance
conjecture\n(which is one of the central open problems in higher dimension
al algebraic\ngeometry) says that if the canonical divisor of a smooth pro
jective\nvariety is nef (i.e. it intersects every curve non-negatively) th
en some\nmultiple of the canonical line bundle is generated by global sect
ions. In\nrecent years\, several abundance-type conjectures have been prop
osed for\ngeneralised pairs. Instead of dealing just with the canonical di
visor K_X\nof a smooth projective variety X\, (roughly speaking) these con
cern\ndivisors of the form K_X+L where L is a nef divisor on X. In this ta
lk\, I\nwill discuss my recent results on generalised abundance \, where I
extend\nsome classical results of Kawamata and Ambro to the setting of ge
neralised\npairs.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.p
y?confId=8626
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8626
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zariski's Finiteness Theorem and Properties of Some Rings of Invar
iants
DTSTART;VALUE=DATE-TIME:20221103T103000Z
DTEND;VALUE=DATE-TIME:20221103T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8635@cern.ch
DESCRIPTION:Abstract: In this talk\, I will present a short proof using a
new idea of a\nspecial case of Oscar Zariski's result about the finite gen
eration in\nconnection with the famous Hilbert's Fourteenth Problem. This
result is\nuseful for invariant subrings of unipotent or connected semisim
ple groups.\nThe next result I will talk about is a stronger form of one w
ell-known\nresult by Andrzej Tyc. This result proves that the quotient spa
ce under a\nregular $\\mathbb{G}_a$-action on an affine space over the fie
ld of complex\nnumbers has at most rational singularities\, under an assum
ption about the\nquotient morphism. If time permits\, I will also sketch t
he main idea of\nthe proof of a result which is an analogue of Masayoshi M
iyanishi's result\nfor the ring of invariants of a $\\mathbb{G}_a$-action
on the polynomial\nring $R[X\, Y\, Z]$ for an affine Dedekind domain $R$.
This proof involves\nsome classical topological methods.\n\nThis talk is b
ased on joint work with R. V. Gurjar and S. R. Gurjar.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=8635
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8635
END:VEVENT
BEGIN:VEVENT
SUMMARY:Background of modular p-adic deformation theory and a brief outlin
e
DTSTART;VALUE=DATE-TIME:20221117T103000Z
DTEND;VALUE=DATE-TIME:20221117T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8652@cern.ch
DESCRIPTION:Abstract: The deformation theory of modular forms is increasin
gly\nattracting many researchers in arithmetic geometry as it has been an\
nimportant step in the proof of Fermat's last theorem by Wiles (and Taylor
)\nand supplied an effective tool for the study of the $p$-adic Birch and\
nSwinnerton Dyer conjecture in the proof by Skinner-Urban of divisibility\
nof the characteristic power series of the Selmer group of a rational\nell
iptic curve by its $p$-adic $L$-function under appropriate assumptions.\n
I try to give my background motivation of creating the theory and\ndescrib
e an outline of the theory.\n\nhttps://indico.tifr.res.in/indico/conferenc
eDisplay.py?confId=8652
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8652
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pencils of quadrics and hyperelliptic curves
DTSTART;VALUE=DATE-TIME:20221123T103000Z
DTEND;VALUE=DATE-TIME:20221123T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8684@cern.ch
DESCRIPTION:Abstract: Connections between the complex geometrry of a hyper
elliptic curve $C$ and the internal geometry of the base locus of the asso
ciated pencil of quadrics are classical and trace back to Andre Weil. Ther
e is a rational description of of the moduli space of rank 2 stable bundle
s with odd determinant on a smooth hyperelliptic curve $C$ of genus $g$ i
n terms of the Grassmannian of $g-1$ dimensional linear subspaces containe
d in the base locus of the associated pencil of quadrics due to Ramanan. W
e explain a twist of this construction which leads to connections between
period index bounds for the unramified Brauer classes on $K(C)$\, $K$ bein
g a totally imaginary number field and the existence of rational points o
n the Grasmannians in the associated pencil of quadrics.\n\nhttps://indico
.tifr.res.in/indico/conferenceDisplay.py?confId=8684
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8684
END:VEVENT
BEGIN:VEVENT
SUMMARY:Shifts of finite type associated to an integer matrix
DTSTART;VALUE=DATE-TIME:20221124T103000Z
DTEND;VALUE=DATE-TIME:20221124T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8675@cern.ch
DESCRIPTION:Abstract: Shifts of finite type are one of the fundamental obj
ects in the field of symbolic dynamics. These are the spaces of one-sided
or two-sided sequences over a finite set of symbols where certain finitely
many words are "forbidden". The shift spaces exhibit a natural associatio
n with $0-1$ matrices. In this talk we will first discuss some necessary p
reliminaries related to the one-sided shifts of finite type associated to
a non-negative integer matrix. Words which correspond to the matrix entrie
s greater than $1$ are thought to have multiplicity and thus are called "r
epeated words". Now\, for any given collection $\\mathcal{F}$ of forbidden
words and $\\mathcal{R}$ of repeated words\, we define two notions: multi
plicity of a word and generalized language. We define the shift determined
by $\\mathcal{F}$ and $\\mathcal{R}$\, and obtain necessary and sufficien
t conditions for when the language of this shift is precisely the generali
zed language. Finally\, we compute the entropy of this shift using the gen
eralized language and study some properties of Markov measures on the shif
t.\n\nThis talk is based on a joint work with Agarwal N. and Haritha C.\n\
nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8675
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8675
END:VEVENT
BEGIN:VEVENT
SUMMARY:n-Selmer group of elliptic curves over number fields
DTSTART;VALUE=DATE-TIME:20221216T090000Z
DTEND;VALUE=DATE-TIME:20221216T100000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8720@cern.ch
DESCRIPTION:Abstract: The recent work of Bhargava et al.\, Mazur-Rubin and
others on\nthe n-Selmer group of an elliptic curve has had a significant\
nimpact on the arithmetic of the elliptic curve. Let E be an elliptic curv
e\nover Q with a rational 3-isogeny. In this talk\, we will discuss the\n3
-Selmer group of E. We will indicate some applications to a\nclassical Di
ophantine problem related to rational cube sum.\n\nThis talk is based on a
joint work with D. Majumdar and P. Shingavekar.\n\nhttps://indico.tifr.re
s.in/indico/conferenceDisplay.py?confId=8720
LOCATION: AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8720
END:VEVENT
BEGIN:VEVENT
SUMMARY:Equivariant Steenrod Operations
DTSTART;VALUE=DATE-TIME:20230112T103000Z
DTEND;VALUE=DATE-TIME:20230112T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8774@cern.ch
DESCRIPTION:Abstract: Classical Steenrod operations is one of the most fun
damental and\nformidable tools in stable homotopy theory. It led to calcul
ation of\nhomotopy groups of spheres\, calculation of cobordism rings\,\nc
haracteristic classes\, and many other celebrated applications of homotopy
\ntheory to geometry. However\, equivariant Steenrod operations are not kn
own\nbeyond the group of order 2. In this talk\, I will demonstrate a geom
etric\nconstruction of the classical Steenrod operations and generalize it
to\nconstruct G-equivariant Steenrod operations for any finite group G. T
ime\npermitting\, I will discuss potential applications to equivariant geo
metry.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId=87
74
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8774
END:VEVENT
BEGIN:VEVENT
SUMMARY:Equivariant vector bundles over toric varieties
DTSTART;VALUE=DATE-TIME:20230119T103000Z
DTEND;VALUE=DATE-TIME:20230119T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8773@cern.ch
DESCRIPTION:Abstract: Toric varieties are equivariant compactifications of
algebraic\ntorus and they come equipped with a rich combinatorial structu
re.\nEquivariant vector bundles over toric varieties have a combinatorial\
nclassification in terms of some linear algebra data. In this talk\, we\nd
iscuss positivity and semi stability of equivariant vector bundles over\nt
oric varieties.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?
confId=8773
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8773
END:VEVENT
BEGIN:VEVENT
SUMMARY:Graded components of local cohomology modules supported on $\\math
frak{C}$-monomial ideals.
DTSTART;VALUE=DATE-TIME:20230202T103000Z
DTEND;VALUE=DATE-TIME:20230202T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8785@cern.ch
DESCRIPTION:Abstract: The structure of local cohomology modules is quite m
ysterious owing to their non-finite generation. Over the last three decade
s\, researchers have extensively investigated if they behave like finitely
-generated modules. Let $A$ be a Dedekind domain of characteristic zero su
ch that its localization at every maximal ideal has mixed characteristic w
ith finite residue field. Let $R=A[X_1\, \\ldots\, X_n]$ be a polynomial
ring equipped with the standard multigrading and let $I\\subseteq R$ be a
$\\mathfrak{C}$-monomial ideal. We call an ideal in $R$ a \\mathfrak{C}$-m
onomial ideal if it can be generated by elements of the form $aU$ where $a
\\in A$ (possibly nonunit) and $U$ is a monomial in $X_i$'s.\nLocal cohom
ology modules supported on usual monomial ideals of a polynomial ring over
a field gain a great deal of interest due to their connections \nwith com
binatorics and toric varieties. The objective of this talk is to discuss a
structure theorem for the multigraded components of the local \ncohomolog
y modules $H^i_I(R)$ for $i \\geq 0$. We will further show that if $A$ is
a PID then each component can be written as a direct sum of its \ntorsion
part and torsion-free part. This result evinces the finiteness of their Ba
ss numbers. This is joint work with Tony J. Puthenpurakal.\n\nhttps://indi
co.tifr.res.in/indico/conferenceDisplay.py?confId=8785
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8785
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enumeration of subwords on sequences and its applications
DTSTART;VALUE=DATE-TIME:20230209T103000Z
DTEND;VALUE=DATE-TIME:20230209T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8800@cern.ch
DESCRIPTION:Abstract: We start with an enumeration problem studied by Guib
as and Odlyzko in 1979 and its applications in seemingly unrelated scenari
os that includes game theory\, pattern matching algorithm\, graph theory a
nd symbolic dynamics. One of the main objects of our study is a subshift o
f finite type\, which is used as a tool to model a large class of dynamica
l systems. It consists of collection of all one-sided sequences over a fin
ite symbol set which contain none of a given finite collection of words. W
e discuss its correspondence with an edge labeled multigraph and hence wit
h its associated adjacency matrix. We see how some (topological as well as
measure theoretic) properties of a subshift of finite type are studied us
ing this correspondence and solve a generalized version of the enumeration
problem.\n\nhttps://indico.tifr.res.in/indico/conferenceDisplay.py?confId
=8800
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8800
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zig-zag is true
DTSTART;VALUE=DATE-TIME:20230216T103000Z
DTEND;VALUE=DATE-TIME:20230216T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8810@cern.ch
DESCRIPTION:Abstract: It is an open problem to describe the shape of the r
eductions of\nlocal Galois representations attached to cusp forms at prime
s away from\nthe level\, or more generally\, the shape of the reductions o
f two-dimensional crystalline representations. Partial results go back to
Deligne\, Fontaine and Edixhoven. One folklore conjecture (attributed to B
reuil\, Buzzard and Emerton) is that if the weight is even and the slope i
s fractional\, then the reduction is always irreducible.\n\nIn this talk w
e shall state and prove our zig-zag conjecture which deals\nwith large exc
eptional weights and half-integral slopes. These weights\nfall squarely ou
tside the scope of the above conjecture. The conjecture states that the re
duction in these cases is given by an alternating sequence of irreducible
and reducible representations depending on the size of two\nauxiliary para
meters.\n\nSpecial cases of zig-zag have been proved over the years by var
ious\nauthors using Langlands correspondences. The present general proof u
ses\nthe reverse of a recent limiting argument due to Chitrao-Ghate-Yasuda
in the\nColmez-Chenevier rigid analytic blow up space of trianguline\nrep
resentations to reduce the study of the reduction of crystalline\nrepresen
tations to results on the reductions of semi-stable\nrepresentations due t
o Breuil-Mezard\, and more recently\, Guerberoff-Park.\n\nhttps://indico.t
ifr.res.in/indico/conferenceDisplay.py?confId=8810
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8810
END:VEVENT
BEGIN:VEVENT
SUMMARY:Relatively hyperbolic groups and convex projective structures
DTSTART;VALUE=DATE-TIME:20230323T103000Z
DTEND;VALUE=DATE-TIME:20230323T113000Z
DTSTAMP;VALUE=DATE-TIME:20230329T103429Z
UID:indico-event-8855@cern.ch
DESCRIPTION:Abstract: Studying discrete subgroups of linear groups using a
preserved\ngeometric structure has a long tradition\, for instance\, usin
g real\nhyperbolic geometry to study discrete subgroups of SO(n\,1). Conve
x\nprojective structures\, a generalization of real hyperbolic structures\
, has\nrecently received much attention in the context of studying discret
e\nsubgroups of PGL(n). In this talk\, I will discuss convex projective\ns
tructures and discuss results (joint with A. Zimmer) on relatively\nhyperb
olic groups that preserve convex projective structures. In\nparticular\, I
will discuss a complete characterization of relative\nhyperbolicity in te
rms of the geometry of the projective structure.\n\nhttps://indico.tifr.re
s.in/indico/conferenceDisplay.py?confId=8855
LOCATION: AG-69
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8855
END:VEVENT
END:VCALENDAR