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SUMMARY:Ewan Cassidy (Durham)
DTSTART:20250114T140000Z
DTEND:20250114T160000Z
DTSTAMP:20260423T023015Z
UID:WienGAGT/42
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WienGAGT/42/
 ">Random permutations\, word maps and Schreier graph expansion</a>\nby Ewa
 n Cassidy (Durham) as part of Vienna Geometry and Analysis on Groups Semin
 ar\n\n\nAbstract\nGiven a word \\(w\\) in the free group on \\(r\\) genera
 tors\, one can obtain a word map for any finite group\, \\(w \\colon\\thin
 space G^r\\to G\\)\, by substitutions. By uniformly randomly sampling \\(r
 \\) random permutations in \\(S_n\\) and evaluating their image under this
  word map\, we obtain a '\\(w\\)-random permutation'. Recent studies of th
 ese random permutations have exposed some deep connections with various ot
 her areas of mathematics. I will discuss the current asymptotic bounds we 
 have for the expected irreducible characters of \\(w\\)-random permutation
 s\, and an application towards showing that a large family of random Schre
 ier graphs have a near-optimal spectral gap with high probability.\n
LOCATION:https://researchseminars.org/talk/WienGAGT/42/
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