Mather classes via small resolutions

Abstract: The Chern-Mather class is a characteristic class, generalizing the Chern class of a tangent bundle of a nonsingular variety to a singular variety. It uses the Nash-blowup for a singular variety instead of the tangent bundle. In this talk, we consider Schubert varieties, known as singular varieties in most cases, in the even orthogonal Grassmannians and discuss the work computing the Chern-Mather class of the Schubert varieties by the use of the small resolution of Sankaran and Vanchinathan with Jones’ technique. We also describe the Kazhdan-Lusztig class of Schubert varieties in Lagrangian Grassmannians, as an analogous result. If time permitted, we discuss the application of Jones’s method on K-orbit closures in flag varieties, as a joint work with Graham and Scott.

algebraic geometrycombinatorics

Audience: researchers in the discipline

MAAGC 2024

Series comments: The 2024 annual Mid-Atlantic Algebra, Geometry, and Combinatorics (MAAGC) Workshop will take place Friday and Saturday, October 11-12, 2024 at The George Washington University in Washington, DC.

The MAAGC Workshop aims to bring together senior researchers and junior mathematicians from the region to exchange ideas and forge collaborations in algebra, geometry, and combinatorics. The conference is funded by National Science Foundation grant DMS-2408985.