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SUMMARY:Spectral gaps for random Schreier graphs - Ewan Cassidy (Universit
 y of Cambridge)
DTSTART:20251008T091500Z
DTEND:20251008T101500Z
UID:TALK236242@talks.cam.ac.uk
DESCRIPTION:I will discuss a generalization of Friedman's theorem\, focusi
 ng on the spectral gap of the random regular Schreier graphs associated wi
 th the action of S_n on K_n--tuples of distinct elements in {1\,...\,n}. T
 he proof relies on the `polynomial method'\, a new approach to strong conv
 ergence of Chen\, Garza--Vargas\, Tropp and van Handel\, combined with new
  group theoretic inputs. A key ingredient is a new asymptotic bound on the
  expected character of a random permutation obtained via a word map\, whic
 h is expressed in terms of the dimension of the corresponding representati
 on.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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