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报告题目：Derived equivalences of algebras and equivalence relations of matrices

报告人：惠昌常 教授（首都师范大学）

报告时间：2024年11月14日(周四)下午14:00-15:00

主持人：朱萍 教授

地点：腾讯会议：318-3268-9875

报告摘要：

Derived (and Morita) equivalences are of great interest in representation theory, For example, one of the central conjectures in modular representations of groups is Broue's abelian defect group conjecture which states that two block algebras under Brauer's correspondence groups are derived equivalent if they have abelian defect groups. In this talk, we investigate derived and Morita equivalences of centralizers of matrices. The study of centralizers of matrices has a long history and can trace back to F.G. Frobenius in 1880's. We introduce new equivalence relations on all square matrices in terms of matrix invariants. In this way, we characterize derived equivalences for centralizer matrix algebras and reduce the study of these derived equivalences to that of problems in linear algebra. The talk reports parts of a joint work with X.G.Li, see arXiv:2312.08794.

主讲人简介：

惠昌常，首都师范大学特聘教授，博士生导师，长江学者特聘教授，博士毕业于联邦德国Bielefeld大学；曾获教育部科技进步二等奖、德国“年轻杰出学者洪堡奖”；在代数表示论、同调代数、导出范畴等学科取得了出色的研究成果, 在Adv.Math、Comm.Math.Phys、Compos.Math、J.Rein Angew.Math、Math.Ann、Proc.LMS、Sci.China Math、Trans.AMS、J.Algebra等国际数学刊物发表论文90多篇，多次在国际代数学术会议作大会报告；主持和参加国家自然科学基金重点项目；任《Journal of Algebra》、《Archiv der Mathematik》等国际数学杂志编委。