Manjul Bhargava

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Using maximal isotropic submodules in a quadratic module over Z p , we prove the existence of a natural discrete probability distribution on the set of isomorphism classes of short exact sequences of co-finite type Z p-modules, and then conjecture that as E varies over elliptic curves over a fixed global field k, the distribution of is that one. We show(More)
Professor Bhargava's work on composition laws revolutionized algebraic number theory, and earned him the Cole Prize in number theory, the SASTRA Ramanujan Prize, and a Clay Research Award, as well as a full professorship at Princeton at the age of 29—just two years after earning his PhD. He is fascinated by mathematical patterns that arise in music and(More)
Faltings' theorem states that curves of genus g > 2 have finitely many rational points. Using the ideas of Faltings, Mumford, Parshin and Raynaud, one obtains an upper bound on the upper bound on the number of rational points [Szp85], XI, §2, but this bound is too large to be used in any reasonable sense. In 1985, Coleman showed [Col85] that Chabauty's(More)
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