题目： On two theorems of Mordell and their legacy

报告人：Loïc, Georges MEREL, Université Paris（巴黎大学）

时间：2025年3月12日，16：00-17：00

地点：东区第五教学楼5406

摘要: Two philosophical attitudes could guide the mathematician in the attempt to solve a problem. According to the more pragmatic school of thought, a researcher should focus exclusively on the simplest situation, and only after a resolution has been found, pass to other cases. The other methodology professes that the problem should be considered at the right level of generality, so as to make a solution appear naturally. We will illustrate this dilemma with two famous theorems of L. Mordell (1888-1972), related conjectures and the subsequent history.  The theorems are central to diophantine geometry (finiteness results for rational point on elliptic curves) and automorphic forms respectively (multiplicative properties of the coefficients of Ramanujan τ function).