Speaker:  Jerson Caro (PUC, Chile)
Date: 028/08/2022 at 10:30
Title: Some advances in a conjecture of Watkins.

Abstract:  In 2002 M. Watkins conjectured that for every elliptic curve defined over \mathbb{Q}, 
its Mordell-Weil rank is at most the 2-adic valuation of its modular degree. In this talk, we will 
show some results with respect to this conjecture and also different approaches to ensure an elliptic 
curve satisfies this conjecture. In addition, we introduce some of the main tools that we use, such as 
Correspondence between elliptic curves and newforms, Atkin-Lehner involutions and their actions on newforms, 
and 2-decent, among others.