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Spectral gap in simple Lie groups : Clay Mathematics Institute Senior Scholar Lecture.

Presented by: 
Y Benoist [Université Paris-Sud 11]
Date: 
Monday 16th June 2014 - 16:00 to 17:00
Venue: 
INI Seminar Room 1
Abstract: 
Consider two matrices a , b in the orthogonal group SO(d) that span a dense subgroup. We will first recall that, in dimension at least 3, for n large, the set of words of length n in a and b become equidistributed in SO(d). We will then see that, when the matrices a, b have algebraic coefficients, the precision of this equidistribution is exponentially small in n. This joint work with N. de Saxce extends previous results of Bourgain and Gamburd for the unitary groups SU(d).
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons