Dr. Olya Mandelshtam, University of Waterloo

Title: Tableaux, Macdonald polynomials, and hopping particles Abstract:

The theory of interacting particle systems is a relatively modern area that has found some unexpected connections to orthogonal polynomials, symmetric functions, and various combinatorial structures. The ASEP (asymmetric simple exclusion process) is one of the most famous such particle models, having a remarkable connection to the Macdonald polynomials P_{\lambda}, which are a family of symmetric functions that have received much attention in algebraic combinatorics. In this talk, we will discuss another particle model called the TAZRP (totally asymmetric zero range process), which has a recently discovered parallel relationship to the modified Macdonald polynomials H_{\lambda}, a combinatorial transformation of P_{\lambda}. We will describe a Markov process on tableaux which makes this relationship explicit. No advanced prior knowledge of probability or symmetric function theory will be assumed. This is joint work with Arvind Ayyer and James Martin.