School of Mathematics Colloquium

Representing hermitian K-theory by orthogonal Grassmannian in A^1-homotopy theory

by Dr. Girja Shanker Tripathi (TIFR)

Thursday, September 15, 2011 from to (Asia/Kolkata)
at Colaba Campus ( AG-69 )
Description
In this talk I will explain a joint work with Marco
Schlichting on geometric representability of hermitian $K$-theory in the
homotopy theory of schemes. After recalling some basic notions from the
homotopy theory of schemes developed by Morel and Voevodsky, I will define
an ind-scheme $GrO$, the orthogonal Grassmannian, and construct a map from
$GrO$ into hermitian $K$-theory $KO$. I will sketch a proof that this map is a
homotopy equivalence and discuss some applications of the result.