摘要

本报告旨在介绍模形式和椭圆曲线这两个数论中的重要概念，及它们之间的密切联系，特别是它们是如何在证明费马大定理中发挥关键作用的。除此之外，本报告还将介绍模形式和椭圆曲线在其他学科中的应用，例如密码学与量子计算等。

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.