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SUMMARY:Strong convergence of typical permutation representations of surfa
 ce groups - Ramon  van Handel (Princeton University)
DTSTART:20251009T130000Z
DTEND:20251009T140000Z
UID:TALK236263@talks.cam.ac.uk
DESCRIPTION:Suppose we draw NxN permutation matrices A\,B\,C\,D uniformly 
 at random fromthe set of all such matrices that satisfy [A\,B][C\,D]=1. Wh
 at can we sayabout the spectral gap of noncommutative polynomials of these
  matrices\,asymptotically as N goes to infinity? I will aim to explain the
  origin ofof such questions of strong convergence\, their implications for
  the studyof spectral gaps of surfaces\, and how a recent new development\
 , thepolynomial method\, now makes it possible to prove such results. This
  talkis based on joint work with Michael Magee and Doron Puder.
LOCATION:Seminar Room 1\, Newton Institute
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