Schubert calculus, TASEP, and free fermions

Speaker: Travis Scrimshaw
Affiliation: Osaka Metropolitan University, Japan

Abstract

In this talk, we will discuss a relationship between:

- the Grassmannian, a classical object from algebraic geometry;

- the Totally Asymmetric Simple Exclusion Process (TASEP), a classical stochastic process; and

- the free fermion Fock space construction.

Starting with K-theoretic Schubert calculus, we will begin by defining the refined dual Grothendieck polynomials using the combinatorics of reverse plane partitions. We then transform the combinatorics into a matrix definition that allows us to describe the transition probabilities of TASEP using a process called last-passage percolation. By using Wick's theorem, we then write the refined dual Grothendieck polynomials as matrix elements using the now-classical fermionic Fock space. This is based on joint work with Kohei Motegi and Shinsuke Iwao. No prior knowledge will be assumed.