Positive m-Divisible Non-crossing Partitions and Their Cyclic Sieving

Explore a 45-minute mathematical lecture that delves into the geometric interpretation of the Kreweras lattice embedding within non-crossing partitions and 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, subject to specific edge conditions from the Cayley graph. Discover the collaborative research findings with Nantel Bergeron, Philippe Nadeau, Hunter Spink, and Vasu Tewari, examining a sub variety of GL/B and its description through the Kreweras lattice. Investigate the non-crossing combinatorics of this space and understand how its cohomology ring connects to various areas of algebraic combinatorics, including quasisymmetric polynomials, Schubert calculus, and the recently introduced forest polynomials by Tewari and Nadeau.