## Discrete Geometry and Combinatorics Seminar

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.