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CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, February 28, 2019 - 3:00pm

Olya Mandelshtam

Brown University


University of Pennsylvania


The multispecies asymmetric simple exclusion process (ASEP) is a model of hopping particles of M different types hopping on a one-dimensional lattice of N sites. In this talk, we consider the ASEP on a ring with the following dynamics: particles at adjacent sites can swap places with either rate 1 or t depending on their relative types. Recently, James Martin gave a combinatorial formula for the stationary probabilities of the ASEP with generalized multiline queues. It turns out that by introducing additional statistics on the multiline queues, we get a new formula for both symmetric Macdonald polynomials P_{\lambda} and nonsymmetric Macdonald polynomials E_{\lambda}, where \lambda is a partition.  This talk is based on joint work with Sylvie Corteel (Universit\'{e} Paris-Diderot) and Lauren Williams (Harvard).