Speaker: Hongxing Chen

Capital Normal University
Title: Homological theory of self-orthogonal modules and Tachikawa's second conjecture
Abstract: In 1970, Hiroyuki Tachikawa proposed two homological conjectures arising from Nakayama's conjecture. Tachikawa's second conjecture says that if a finitely generated module over a self-injective Artin algebra is self-orthogonal, then it is projective. In this talk, we first discuss some homological properties of self-orthogonal generators over self-injective algebras in terms of the stable categories of Gorenstein projective modules over their endomorphism algebras, and then provide several equivalent characterizations of Tachikawa's second conjecture. It turns out that a class of generalized symmetric algebras (that is, endomorphism algebras of generators over symmetric algebras) is shown to satisfy Nakayama's conjecture. This is based on an ongoing work with Professor Changchang Xi.

Time：27 Nov 2019, 8:30

Location：实验楼105

Speaker  Introduction：陈红星，德国洪堡访问学者。本科就读于湖南师范大学，博士毕业于北京师范大学，2011-2013年在北京大学国际数学研究中心从事博士后研究，2013年8月至今在首都师范大学任教。曾获教育部学术新人奖，入选’’北京市科技新星计划”, 主持过国家自然科学基金青年项目、北京市自然科学基金青年项目、中国博士后科学基金项目，参与过国家自然科学基金重点项目和北京市教育委员会科技计划重点项目。主要从事代数表示论和同调代数的研究，在同调猜想、导出范畴、无限维倾斜理论、代数K-理论等方面取得了一系列的研究成果，彻底解决Angeleri-Huegel、Koenig和Liu提出的关于导出模范畴Jordan-Hölder定理存在性问题。研究成果发表在Proc. Lond. Math. Soc.、Int Math Res Notices、Forum Math、J. London. Math. Soc.等国际知名数学杂志上。

联系人：陈健敏副教授