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{\Large Department of Mathematics, BGU}

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{\Huge Colloquium}\\[0.2\baselineskip]

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\textbf{On} \emph{Tuesday, January 20, 2026}
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\textbf{At} \emph{14:30 -- 15:30}
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\textbf{In} \emph{Math -101}

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{\large\scshape Itay Glazer 
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  (Technion)
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will talk about
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{\Large\bfseries Mixing of conjugacy classes and character estimates\par}
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\textsc{Abstract:}
In 1981, Diaconis and Shahshahani showed that roughly n*log(n) random transpositions are required to mix a deck of n cards (namely, to produce an approximately random permutation in S\_n). In their work, they translated this problem into a question in the representation theory of the symmetric group S\_n, about bounding the values of irreducible characters at a transposition t = (i j).
In this talk, I will explain how this perspective extends far beyond card shuffling; For a finite or compact group G, one can ask how quickly repeated multiplication by a fixed conjugacy class becomes uniformly distributed, and how this problem is controlled by general character estimates. I will describe this general framework, survey some known results, and discuss recent progress on character bounds in unitary groups. 
Based on a joint work (in progress) with Nir Avni, Peter Keevash and Noam Lifshitz and on a work with Nir Avni and Michael Larsen (arXiv:2402.11108).








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