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Number Theory Seminar

Monday, March 27th, 2023

Time: 4:30 p.m.  Place: Jeffery Hall, Room 319

Speaker: Dominic Austria (³ÉÈË´óƬ)

Title: Congruent Numbers and Tunnell’s Theorem

Abstract: We will discuss congruent numbers, their relation to elliptic curves, and some known results about the congruent number problem. The focus will be on outlining the proof of Tunnell’s theorem. We discuss the key tools needed for this--the L-function of a particular elliptic curve associated with the congruent number problem, and modular forms, of both integer weight and half integer weight. We will then see how results on both of these topics can be combined, using the theorems of Shimura and Waldspurger, to classify the congruent numbers up to conjecture.