Title: Formulas for Macdonald polynomials arising from the ASEP
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The asymmetric simple exclusion process (ASEP) is a one-dimensional model of hopping particles that has been extensively studied in statistical mechanics, probability, and combinatorics. It also has remarkable connections with orthogonal symmetric polynomials in many variables such as Macdonald and Koornwinder polynomials. In this talk, I will discuss new formulas for Macdonald polynomials (joint work with Corteel and Williams) that arise from the study of the ASEP on a ring, and introduce a new notion of quasisymmetric Macdonald polynomials (joint with Corteel, Haglund, Mason, and Williams) that specialize to the quasisymmetric Schur polynomials defined by Haglund, Luoto, Mason, and van Willigenburg.