Dominic Austria (Queen's University)
Date
Monday March 27, 20234:30 pm - 5:30 pm
Location
Jeffery Hall, Room 319Event Category
Number Theory Seminar
Monday, March 27th, 2023
Time: 4:30 p.m. Place: Jeffery Hall, Room 319
Speaker: Dominic Austria (Queen's University)
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.