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线上学术报告

Title: From algebraically closed fields to arbitrary fields

Speaker: 周远扬教授（华中师范大学）

Abstract

Broué conjecture is one of the most important conjectures in the representation theory of finite groups. Broué conjecture over algebraically closed fields is due to M. Broué. Chuang and Rouquier proved that the conjecture (actually over arbitrary fields) holds for symmetric groups and general linear groups (2008). By the work of Chuang and Rouquier, it was observed that the conjecture might hold for arbitrary fields. Then Craven and Rouquier investigated this observation (2013) and they proved that Broué conjecture over arbitrary fields holds for principal blocks for finite groups with abelian Sylow 2-subgroups and with Sylow 3-group of order 9. Inspired by Galois-Alperin-McKay conjecture due to Navarro, Linckelmann formally raised Broué conjecture over arbitrary fields (2018) and proved that Broué conjecture over arbitrary fields holds for cyclic blocks. However, all these investigations above for Broué conjecture over arbitrary fields are case by case. In this talk, we aim to generally study Broué conjecture from over algebraically closed fields to over arbitrary fields. As a consequence of this study, we prove that Puig’s finiteness conjecture for nilpotent blocks is true. Puig’s finiteness conjecture for nilpotent blocks itself is a longstanding conjecture. Even more generally, we prove that Puig’s finiteness conjecture holds for inertial blocks.

报告人简介：周远扬，华中师范大学教授，博士生导师，洪堡学者。现为《数学通讯》主编、《Algebra Colloquium》编委。2008年入选教育部新世纪优秀人才支持计划，2016年获国家自然科学基金杰出青年科学基金资助。主要研究块代数的结构性质及其分类，主要研究课题有Alperin权猜想、Alperin-McKay猜想、Broué交换亏群猜想等。

北京时间：2022年10月6日（周四）上午9:00-10:00

腾讯会议：770-3833-5039  会议密码:  202210

入会链接:  https://meeting.tencent.com/dm/KDcuUQFL08o8

联系人:  惠昌常 陈红星