School of Mathematics Seminars and Lectures

Affine Deligne-Lusztig Varieties and Quantum Bruhat Graph

by Dr. Arghya Sadhukhan (University of Maryland)

Wednesday, June 8, 2022 from to (Asia/Kolkata)
at AG-77
Description
Abstract: The study of affine Deligne-Lusztig varieties (ADLVs) X_w(b) and their certain union X(\mu,b) arose from the study of Shimura varieties with Iwahori level structure. As such, understanding their structural properties has been crucial in studying reductions of Shimura varieties in the context of arithmetic geometry. On the other hand, first introduced in enumerative geometry to describe the quantum cohomology ring of a complex flag variety, quantum Bruhat graphs have proved to be useful in recent years in certain Lie-theoretic and arithmetic-geometric problems. For instance, they encode covering relations in affine Weyl group and give rise to useful description of the admissible set and the Demazure product; these in turn allow us to understand the generic Newton point in Iwahori double cosets in loop groups and hence find applications in the problem of dimensions and irreducible components of certain ADLVs. We will discuss these recent developments and report on some ongoing work.