報告題目：Derived equivalences of algebras and equivalence relations of matrices
報告人：惠昌常 教授（首都師范大學(xué)）
報告時間：2024年11月14日(周四)下午14:00-15:00
主持人：朱萍 教授
地點：騰訊會議：318-3268-9875
報告摘要：
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.
主講人簡介：
惠昌常，首都師范大學(xué)特聘教授，博士生導(dǎo)師，長江學(xué)者特聘教授，博士畢業(yè)于聯(lián)邦德國Bielefeld大學(xué)；曾獲教育部科技進步二等獎、德國“年輕杰出學(xué)者洪堡獎”；在代數(shù)表示論、同調(diào)代數(shù)、導(dǎo)出范疇等學(xué)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等國際數(shù)學(xué)刊物發(fā)表論文90多篇，多次在國際代數(shù)學(xué)術(shù)會議作大會報告；主持和參加國家自然科學(xué)基金重點項目；任《Journal of Algebra》、《Archiv der Mathematik》等國際數(shù)學(xué)雜志編委。
