Advanced GMA Seminar – Speaker: Josh Kiers – A survey of the BGG description of cohomology of flag varieties, with applications

Speaker: Josh Kiers

Part 1: A survey of the BGG description of cohomology of flag varieties, with applications

Abstract: In these lectures we will follow the original paper of Bernstein, Gel’fand, and Gel’fand (Schubert cells and cohomology of the spaces G/P) which identifies the cohomology of flag varieties W-equivariantly with certain (sub)quotients of explicit polynomial rings. We will develop the Lie combinatorics necessary to identify (and prove) “good” polynomial representatives with their Schubert class counterparts, along the way introducing the Bruhat order and the famous divided-difference operators. We will develop an “integration” formula by way of application, and I will explain how I used this in a crucial way for computer verification of two new instances of the Saturation Conjecture.