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Joint Berkeley-Caltech-Stanford Number Theory Seminar

Monday, October 19, 2020
12:30pm to 2:00pm
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Irreducibility of random polynomials with large degree
Emmanuel Breuillard, Department of Pure Mathematics and Mathematical Statistics, University of Cambridge,

I will discuss properties of random polynomials with integer coefficients and large degree. Modulo GRH we show with Peter Varju that they are irreducible modulo cyclotomic factors, thus offering a conditional answer to a question of Odlyzko and Poonen. The proof is based on an understanding of mixing rates of random walks on the affine line over large finite fields and has connections with the Lehmer conjecture.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].