# Colloquium abstracts

**Aditya Subramaniam**

TIFR, Mumbai

March 3, 2022

**Some results on Seshadri constants**: 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.