Some results on Seshadri constants

Abstract: Seshadri constants were defined by Demailly as a local measure
of positivity of line bundles. He introduced this notion motivated by
Seshadri's ampleness criterion for line bundles. Later, Hacon generalized
the notion of Seshadri constants to vector bundles. Seshadri constants
have now become a central object of study in numerous directions in
algebraic geometry, particularly in the study of linear series. In
general, Seshadri constants are hard to compute and a lot of research is
aimed at finding good estimates.

In this talk, we will start with basics on Seshadri constants and discuss
some important results and connections to well known questions. We will
then focus on computing Seshadri constants for some torus equivariant
vector bundles at arbitrary points on projective spaces and Bott towers of
height at most 3. This is based on a joint work with Jyoti Dasgupta and
Bivas Khan.