报告人：Dougal Davis（墨尔本大学）

时 间：2023年5月25日8:30-10:00

地 点：Zoom会议ID：886 4764 1038（密码:560843）

内容摘要:

I will explain an ongoing program, joint with Kari Vilonen, that aims to make progress towards the classification of unitary representations of real reductive Lie groups using mixed Hodge modules on flag varieties. The program revolves around a conjecture of Schmid and Vilonen that irreducible representations carry canonical polarised Hodge structures. The conjecture implies that unitarity can be read off from properties of a geometrically defined filtration, the Hodge filtration. While the full conjecture is still open, I will sketch a proof of this main consequence (currently in preparation), which is likely to be all that is required for applications. The proof builds on several of our previous results linking Hodge theory to the unitarity algorithm of Adams, van Leeuwen, Trapa and Vogan.

个人简介：

Dr. Davis works on mathematical problems at the interface between algebraic geometry and representation theory. He completed his PhD in 2019 from King’s College London under the supervision of Prof Nicholas Shepherd-Barron. From 2019 to 2022, he was a postdoctoral research associate at the University of Edinburgh, and is now a research fellow at the University of Melbourne. He has published his paper in Pure and Applied Mathematics Quarterly.

联系人：余世霖