Cotangent Schubert Calculus and Cohomology Rings in Flag Varieties

Explore advanced mathematical concepts in this one-hour lecture on Cotangent Schubert Calculus delivered at the Institute for Advanced Study. Delve into the study of cohomology rings in generalized flag varieties, examining their fundamental classes of Schubert varieties and distinctive structural properties. Learn about alternative bases derived from characteristic classes of singular varieties, including Chern-Schwartz-MacPherson classes for Schubert cells in cohomology and motivic Chern classes in K-theory. Discover how these bases relate to the Schubert basis through Hecke algebra, and understand their connections to positivity statements and Kazhdan-Lusztig theory. Examine recent developments in the field based on collaborative research with P. Aluffi, J. Schurmann, and C. Su, while exploring outstanding questions in this specialized area of mathematics.