Algebraic and Enumerative Combinatorics - Olya Mandelshtam

Thursday, April 4, 2024 2:00 pm - 3:00 pm EDT (GMT -04:00)

Title: A new formula for the symmetric Macdonald polynomials via the ASEP and TAZRP

Speaker: Olya Mandelshtam
Affiliation: University of Waterloo
Location: MC 5479

There will be a pre-seminar presenting relevant background at the beginning graduate level starting at 1pm.

Abstract: In this talk, I will describe some recently discovered connections between one-dimensional interacting particle models (the ASEP and the TAZRP) and Macdonald polynomials and show the combinatorial objects that make these connections explicit. I will give a new compact tableau formula for the symmetric Macdonald polynomials $P_{\lambda}(X;q,t)$ in terms of a queue inversion statistic on certain sorted non-attacking tableaux. The nonsymmetric components of our formula specialize to the probabilities of the asymmetric simple exclusion process (ASEP) on a circle; moreover, the queue inversion statistic is naturally related to the dynamics of the ASEP. The new formula arises from the plethystic correspondence between the classical and modified Macdonald polynomials, which is closely related to fusion in the setting of integrable systems which connects the ASEP to the TAZRP.