Abstract

In this lecture, I will introduce modular forms and elliptic curves, two important notions from number theory, as well as their close relationship.  In particular, I will explain how they played a key role in the proof of Fermat’s Last Theorem.  Moreover, I will discuss applications of modular forms and elliptic curves to other disciplines, such as cryptography and quantum computing.

Ruochuan Liu is a Boya Distinguished Professor in mathematics of Peking University and a New Cornerstone Investigator.  His current research focuses on p-adic aspects of arithmetic geometry and number theory, especially p-adic Hodge theory, p-adic automorphic forms and related topics.  In 2017, he received the National Natural Science Fund for Distinguished Young Scholars.  He was awarded the Tencent Xplorer prize in 2019 and the second prize of the National Award for Natural Sciences in 2020.