Non-crossing Partitions, Equivariant Cohomology, and Polynomials

Explore a mathematical lecture that delves into the geometric interpretation of the Kreweras lattice embedding within the Cayley graph of the symmetric group. Learn how toric geometry presents the equivariant cohomology ring of the flag variety GL/B through polynomial-valued functions on the symmetric group, constrained by Cayley graph edge conditions. Discover research findings from a collaboration with Nantel Bergeron, Philippe Nadeau, Hunter Spink, and Vasu Tewari that identifies a sub variety of GL/B described through the Kreweras lattice. Examine the non-crossing combinatorics of this space and understand how its cohomology ring connects to algebraic combinatorics, including quasisymmetric polynomials, Schubert calculus, and the recently developed forest polynomials by Tewari and Nadeau.