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Primes, Polynomials and Random Matrices

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The Prime Number Theorem tells us roughly how many primes lie in a given long interval. We have much less knowledge of how many primes lie in short intervals, and this is the subject of a conjecture due to Goldston and Montgomery. Likewise, we also have much less knowledge of how many primes lie in different arithmetic progressions. This is the subject of a conjecture due to Hooley. I will discuss the analogues of these conjectures for polynomials defined over function fields and outline how they can be proved using the theory of random matrices.

This talk is part of the Discrete Analysis Seminar series.

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