Tutte Colloquium - Olya Mandelshtam

Title: Macdonald polynomials and the multispecies zero range process

Abstract:

Over the last couple of decades, the theory of special functions and symmetric functions have found unexpected connections to various interacting particle systems. Macdonald polynomials are a family of symmetric functions that are known to have remarkable connections to a well-studied particle model called the ASEP. It is natural to ask whether the modified Macdonald polynomials can be obtained using a combinatorial gadget for some other particle system. In this talk, we answer this question in the affirmative with a certain multispecies zero-range process that we call TAZRP. This link leads to a new formula for modified Macdonald polynomials in terms of tableaux. We present a Markov process on these tableaux that projects to the TAZRP, giving us a formula for the stationary distribution. This talk is based on joint work with Arvind Ayyer and James Martin.