Algebraic and Enumerative combinatorics seminar -Alexandre Zotine-A pipe dream framework for orbital varieties of type M² = 0

Abstract: An orbital scheme D of type M² = 0 is the closure of a conjugacy class of some set of n × n upper triangular matrices which are nilpotent of order 2. The geometric components of the orbit scheme are called orbital varieties of type M² = 0, and recently their invariants have been connected to statistical mechanics. In the setting of M² = 0, there are combinatorial methods for studying these invariants via the action of the Borel group of upper triangular invertible matrices. In this talk, we introduce a new pipe dream framework for computing and understanding these invariants. This is joint work with Megumi Harada, Illya Kierkosz, Allen Knutson, Emma Naguit, Brett Nasserden, Naveena Rangunathan, and Adam van Tuyl.

There will be a pre-seminar presenting relevant background at beginning graduate level starting at 1:30pm in MC 5417.