Time: 14:00-15:00, Friday, March 21 2025
Venue: E4-233, Yungu Campus
Host：Emmanuel Lecouturier, ITS
Speaker：Loïc Merel, Université Paris Diderot
Biography：After studying at École Normale Supérieure in Paris, Merel has obtained a PhD from Sorbonne Université in 1993 (then UPMC-Paris 6). After holding researcher positions at CNRS and UC Berkeley, he has been professor at Université Paris Cité since 1997. Merel was chairman of the large joint department of both Sorbonne Université and Paris Cité from 2016 to 2020. His research focuses on number theory, in particular the arithmetic of automorphic forms, with applications to diophantine geometry, for instance the proof of the Uniform Boundedness Conjecture for elliptic curves.
Title：The Emergence of the Eisenstein Ideal Theory
Abstract: The «Eisenstein ideal» concept follows from congruences between cusp forms and Eisenstein series. The primordial and illustrious example resides in Ramanujan's congruence : if one expands the infinite product q∏m (1-qm)24 as a series ∑n τ(n)qn, τ(n) turns out to be congruent to ∑d|n d modulo 691.
As part of the theory of modular forms, these notions have been invaluable for both arithmetic geometry and algebraic number theory.
The arithmetical geometry side has roots that far predates Ramanujan in the method of descent. We will highlight some of the developments throughout the 20th century that led to the crowning achievement in Mazur's torsion theorem of 1977. This side of the story ended in the mid 1990's.
The algebraic number theory side is a continuing story. We will describe how it led to current research.
