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Mathematics Class of 1960s Speaker: Equidistribution for Elliptic Curves by Prof. Chantal David, Concordia Univrsity, Friday, September 14, 1 – 1:45 pm, Thompson Physics 203

Friday, September 14th, 2018
1:00 pm

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Mathematics Class of 1960s Speaker: Equidistribution for Elliptic Curves by Prof. Chantal David, Concordia University, Friday, September 14, 1 – 1:45 pm, Thompson Physics 203

Abstract:  We present in this talk several natural prime counting conjectures associated to elliptic curves over Q, concerning the reductions of a fixed elliptic curve E over the finite fields F_p, varying over all primes p. Among such conjectures is the Sato-Tate conjecture, which was proven recently by Taylor, in collaboration with Clozel, Harris and Shepherd-Barron. His breakthrough work (recognized by the 2015 Breakthrough Prize in Mathematics!) proves a non-effective version of the Sato-Tate conjecture. We explain in this talk how assuming more hypotheses leads to an effective version of the Sato-Tate conjecture. As an application, we show how this effective version of the Sato-Tate conjecture gives upper bounds for other prime counting conjectures associated to elliptic curves over Q which are still open, such as the Lang-Trotter conjecture and the extremal primes conjecture. This last part is joint with collaborators A. Gafni, N. Prabhu, A. Malik and C. Turnage-Butterbaugh.

The talk will be accessible to a general audience of mathematicians, not only number theorists.

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