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Given a prime p, let P(t) be a non-constant monic polynomial in t over the ring of p-adic integers. Let X(n) be an n x n uniformly random (0,1)-matrix over the same ring. We compute the asymptotic distribution of the cokernel of P(X(n)) as n goes to infinity. When P(t) is square-free modulo p, this […] |
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Given votes for candidates, what is the best way to determine the winner of the election, if some of the votes have been corrupted or miscounted? As we saw in […] |
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Discrete Calculus studies discrete structures, such as sequences and graphs, using techniques similar to those used in Calculus for continuous functions. The basic idea of generating functions is to associate […] |
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It is elementary and well known that a nonzero polynomial in one variable of degree d with coefficients in a field F has at most d zeros in F. It […] |
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We prove, in this joint work with Maksym Radziwill, a 1978 conjecture of S. Patterson (conditional on the Generalized Riemann Hypothesis) concerning the bias of cubic Gauss sums. This explains […] |
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In a remarkable series of papers Zlil Sela classified the first-order theories of free groups and torsion-free hyperbolic groups using geometric structures he called towers, and independently Olga Kharlampovich and Alexei Myasnikov did the same using equivalent structures they called regular NTQ groups. It was later proved by Chloé Perin that if H is an […] |
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