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SUMMARY:Uniform spectral gaps for group actions - Emmanuel Breuillard (Uni
 versity of Oxford)
DTSTART:20251006T091500Z
DTEND:20251006T101500Z
UID:TALK236212@talks.cam.ac.uk
DESCRIPTION:I will present recent and on-going joint work with Oren Becker
  on spectral gaps for actions of linear groups and consequences regarding 
 expander graphs. We prove a uniform spectral gap (uniform Kazhdan constant
  for quasi-regular representations) for all strongly irreducible actions o
 f linear groups on projective and affine spaces. This strong uniformity (w
 .r.t. the generating set and the field of coefficients) has its source in 
 diophantine considerations and the theory of heights. It allows to obtain 
 uniform expansion for finite simple groups of Lie type of bounded rank ove
 r almost all primes as well as uniform non-concentration estimates &agrave
 \; la Littlewood-Offord for random walks on matrix groups.
LOCATION:Seminar Room 1\, Newton Institute
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