Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Fall 2017

Speaker:  Olya Mandelshtam, Brown University
Title: Combinatorics of hopping particles and rhombic tableaux
Time: 2:30 PM, Monday, November 20, 2017
Place:  Malott 206

Abstract: The asymmetric simple exclusion process (ASEP) is a Markov chain from statistical physics that describes the dynamics of particles hopping right and left on a finite 1D lattice with open boundaries. The ASEP displays rich combinatorial structure: one can compute the stationary probabilities for the ASEP using fillings of certain tableaux which are in bijection with permutations. These results have been generalized to the two-species ASEP, and have been recently extended to the two-species ASEP with periodic boundary conditions. In this talk, we will discuss some of the combinatorial objects and bijections related to variations of the ASEP. We will conclude with a remarkable connection to orthogonal polynomials. This talk is based on joint work with X. Viennot and separately with S. Corteel and L. Williams.

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