题目：On the Arthur-Barbasch-Vogan conjecture

报告人：朱程波教授(National University of Singapore)

报告时间：2024年8月3日16:00-17:00

地点：维格堂319

报告摘要：

In this lecture, I will discuss the resolution of the Arthur-Barbasch-Vogan conjecture on the unitarity of special unipotent representations for any real form of a connected reductive complex Lie group, with contributions by several groups of authors (Barbasch-Ma-Sun-Zhu, Adams-Arancibia-Mezo, and Adams-Miller-van Leeuwen-Vogan). The representations concerned originated in Arthur’s conjecture on L2 automorphic forms and were defined by Barbasch-Vogan in the 1980’s. Their unitarity has been a mystery since that time. The main part of the lecture will be on the approach of the first group of authors for the case of real classical groups: (algebraically) counting, (analytically) constructing and (geometrically) distinguishing representations, resulting in a full classification, and with unitarity as a direct consequence of the construction.

The lecture will be targeted at non-specialists and will therefore be non-technical.

报告人简介:朱程波教授1990年博士毕业于美国耶鲁大学,现任新加坡国立大学数学系讲座教授。朱程波教授长期致力于实李群表示论的研究,在theta对应理论、典型群重数一猜想及典型群的特殊幂幺表示等领域做出了重大贡献，相关研究成果发表在Ann. Math.和J. Amer. Math. Soc.等国际著名杂志上。朱程波教授在2009至2012年期间担任新加坡数学会理事长，2014至2020年期间担任新加坡国立大学数学系系主任，2014年当选新加坡国家科学院院士, 2022年受邀在国际数学家大会(ICM)上作45分钟报告。

邀请人：白占强,董超平