报告题目（一）: From algebraically closed fields to arbitrary fields

报告时间: 2022年12月14日(周三)下午3点

报告地点: 腾讯会议 109-221-859

报告摘要: 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 and Feit’s conjecture for inertial blocks are true.

报告人简介: 周远扬，华中师范大学数学与统计学学院教授，院长，湖北省数学会常务理事。洪堡学者，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, 研究成果发表在Advances in Mathematics、Proceedings of the American Mathematical Society、Mathematische Zeitschrift、Journal of Algebra等国际知名期刊上.

报告题目（二）: Derived recollements for infinitely generated tilting module

报告时间: 2022年12月14日(周三)下午4点

报告地点: 腾讯会议 109-221-859

摘要: Tilting theory is one of the most important theories in the representation theory of algebras. In the general context of tilting theory, a central theme is to study relations between the derived module categories of the given algebras and the endomorphism algebras of tilting modules. In the talk, we introduce symmetric subcategories and show that for any good tilting module T over an algebra A, the derived category of the endomorphism algebra B of T is a recollement of the derived categories of A and a symmetric subcategory of the module category of B, in the sense of Beilinson-Bernstein-Deligne. Thus the kernel of the total left-derived tensor functor induced by a good tilting module is always triangle equivalent to the derived category of a symmetric subcategory of a module category. Explicit description of symmetric subcategories associated to a class of good 2-tilting modules over commutative Gorenstein local rings are presented. This is joint work with Changchang Xi.

报告人简介: 陈红星，首都师范大学教授，2021年获国家自然科学基金优秀青年科学基金。曾获教育部学术新人奖，入选北京市科技新星计划。曾主持国家自然科学基金面上、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，并参与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，彻底解决了关于导出模范畴Jordan-Holder定理存在性问题。 研究成果发表在Proc. Lond. Math. Soc., J. London. Math. Soc., Math. Proc. Cambridge Philos. Soc., Israel J. Math., Int Math Res Notices, J. Algebra 等国际知名数学杂志。

报告题目（三）: Deformations and homotopy theory of operated algebras

报告时间: 2022年12月14日(周三)下午5点

报告地点: 腾讯会议 109-221-859

报告摘要: Minimal models of algebras originated from rational homotopy theory and play an important role in algebra. For algebraic structures, it is also important to seek minimal models, say, homotopy version of them. For instance, A-infinity algebras are the homotopy version of associative algebras, which can be obtained by Koszul duality. However, for operated algebras such Rota-Baxter algebras or differential algebras with nonzero weights, the minimal models remained open. Recently we found a method to produce minimal models for such operated algebras. This talk is a survey about recent work on this subject.

报告人简介: 周国栋，华东师范大学数学科学学院副院长、教授，博士毕业于法国亚棉大学，师从著名代数学家Alexander Zimmermann教授。主要研究领域为代数表示论与同调代数。完成国家自然科学基金青年基金、上海市浦江人才计划项目、教育部博士点新教师基金，主持在研国家自然科学基金面上项目两项，其学术成果发表在 J. London Math. Soc.、Math. Z.、Trans. Amer. Math. Soc.、IMRN、J. Algebra、J. Noncommut. Geom. Proc. Royal Edinburgh Soc. Section A: Math.等国际著名期刊上。目前主要学术兼职有美国数学评论员与欧洲数学会评论员。