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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240404T140000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-olya-mandelshtam
SUMMARY:Algebraic and Enumerative Combinatorics - Olya Mandelshtam
CLASS:PUBLIC
DESCRIPTION:TITLE: A new formula for the symmetric Macdonald polynomials vi
 a the\nASEP and TAZRP\n\nSPEAKER:\n Olya Mandelshtam\n\nAFFILIATION:\n Uni
 versity of Waterloo\n\nLOCATION:\n MC 5479\n\nThere will be a pre-seminar 
 presenting relevant background at the\nbeginning graduate level starting a
 t 1pm.\n\nABSTRACT: In this talk\, I will describe some recently discovere
 d\nconnections between one-dimensional interacting particle models (the\nA
 SEP and the TAZRP) and Macdonald polynomials and show the\ncombinatorial o
 bjects that make these connections explicit. I will\ngive a new compact ta
 bleau formula for the symmetric Macdonald\npolynomials $P_{\\lambda}(X\;q\
 ,t)$ in terms of a queue inversion\nstatistic on certain sorted non-attack
 ing tableaux. The nonsymmetric\ncomponents of our formula specialize to th
 e probabilities of the\nasymmetric simple exclusion process (ASEP) on a ci
 rcle\; moreover\, the\nqueue inversion statistic is naturally related to t
 he dynamics of the\nASEP. The new formula arises from the plethystic corre
 spondence\nbetween the classical and modified Macdonald polynomials\, whic
 h is\nclosely related to fusion in the setting of integrable systems which
 \nconnects the ASEP to the TAZRP.
DTSTAMP:20260405T045106Z
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