吴峙佑 博士,Beijing International Center for Mathematical Research

Shimura varieties are a class of algebraic geometric spaces that play a very important role in arithmetic geometry, especially in the Langlands program. In recent years, methods from the geometric representation theory have been introduced in this field, most notably by Liang Xiao and Xinwen Zhu, providing fruitful new perspectives. On the other hand, Peter Scholze has developed a completely new p-adic geometry based on the theory of perfectoid spaces, which has been used with great success in his work with Laurent Faruges to establish one direction of the local Langlands correspondences. I will describe how these revolutionary developments together lead to advances in the theory of Shimura varieties and related fields. In particular, I will talk about how it leads to a proof of Xiao-Zhu's S=T conjecture and the Blasius-Rogawski conjecture.