Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

Schubert calculus transforms the intersection theory of the flag variety $GL_n/B $ into a multiplication problem for combinatorial polynomials, while double Schubert calculus extends this to a torus-equivariant setting. Two essential components underlie these approaches: (1) a surjective homomorphism from the polynomial ring $F[x_1,…,x_n] $ to the (torus-equivariant) cohomology ring of $GL_n/B$, and (2) the existence of Schubert polynomials, a basis of $F[x_1,…,x_n]$ that interacts naturally with the surjection from (1). This talk will describe a subvariety of $GL_n/B $ that exhibits a surprisingly tight analogue of (1) and (2) with respect to another basis of combinatorial polynomials, and moreover generalize this basis to the “double” (equivariant) setting.  I will show how these new objects can be understood with combinatorial objects such as noncrossing partitions and binary trees and then speculate about how this might deepen our understanding of Schubert calculus. No prior knowledge of the subject will be assumed.  This is based on an ongoing project with Nantel Bergeron, Philippe Nadeau, Hunter Spink, and Vasu Tewari.

Note the special time (noon) and room (2112) , but we also have ADM at the usual 3pm time that Friday