Video Lectures

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A k-modal probability distribution over the domain {1,...,N} is one whose histogram has at most k "peaks" and "valleys". Such distributions are a natural generalization of the well-studied class of monotone increasing (or monotone decreasing)...

Inspired by the theory of good lattice points in numerical integration, Zaremba conjectured in 1972 that for every denominator q, there is some coprime numerator p, such that the continued fraction expansion of p/q has uniformly bounded quotients...

I will talk about a joint work with Jean Bourgain that establishes spectral gaps for random walks on SL_n(Z/qZ). Let S be a fixed finite and symmetric subset of SL_n(Z) which generates a Zariski dense subgroup. We show that words of length C log...