题目：CHARACTERIZATION OF BALL QUOTIENT VIA THE SIMPSON-MOCHIZUKI THEORY

报告人：邓亚，法国高等科学研究所(IHES)

时间：2020年7月14,16日下午3:00-4:30

ZOOM 会议号: 567 388 6143 (无需密码参会)

摘要：

Theory of Higgs bundles, introduced by Hitchin and Simpson in 1980s, is one of the most important discoveries in mathematics. It has a rich structure and play a role in many different areas. In 1988, Simpson extended Donaldson-Uhlenbeck-Yau theorem to the context of Higgs bundles, and he applied his theorem to construct variation of Hodge structures using Hermitian-Yang-Mills metrics. As a fascinating application, he gave a characterization for compact Hermitian locally symmetric varieties, in particular for compact ball quotient. It is thus quite natural to ask whether one can extend his characterization to non-compact setting. The goal of this three-hour talk is to explain the speaker’s recent progress on this problem. 

This series of lectures will be divided into 2 parts. Lecture 1 is focused on the basic theory on Higgs bundles by Simpson and its log generalization by Mochizuki. In Lecture 2 Doctor Deng shall explain how to apply their deep work to construct variation of Hodge structures over quasi-projective varieties. This shall be used to achieve their ultimate goal: to characterize non-compact ball quotient and its toroidal compactification.