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UID:20260407T070828EDT-1650cvHMK1@132.216.98.100
DTSTAMP:20260407T110828Z
DESCRIPTION:Titre: Spectrum of random-to-random shuffling in the Hecke alge
 bra\n\nRésumé: The eigenvalues of a Markov chain determine its mixing time
 . In this talk\, I will describe a Markov chain on the symmetric group cal
 led random-to-random shuffling whose eigenvalues have surprisingly elegant
 —though mysterious—formulas. In particular\, these eigenvalues were shown 
 to be non-negative integers by Dieker and Saliola in 2017\, resolving an a
 lmost 20 year conjecture.\n\nIn recent work with Ilani Axelrod-Freed\, Jud
 y Chiang\, Patricia Commins and Veronica Lang\, we generalize random-to-ra
 ndom shuffling to a Markov chain on the Type A Iwahori Hecke algebra\, and
  prove combinatorial expressions for its eigenvalues as a polynomial in q 
 with non-negative integer coefficients. Our methods simplify the existing 
 proof for q=1 by drawing novel connections between random-to-random shuffl
 ing and the Jucys-Murphy elements of the Hecke algebra.\n\nLocation: Local
 : PK-4323\n
DTSTART:20241011T150000Z
DTEND:20241011T160000Z
SUMMARY:Sarah Brauner (UQAM & Brown University)
URL:https://www.mcgill.ca/mathstat/channels/event/sarah-brauner-uqam-brown-
 university-360256
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