2024年第3期第22讲：朱彬教授学术报告

广州数学大讲坛第三期

第二十二讲——清华大学朱彬教授学术报告

题目：Supportτ-tilting subcategories in exact categories

时间：2024年4月22日（周一）09：30-11：00

地点：理学实验楼312

报告人：朱彬教授

摘要：Let E = (A, S) be an exact category with enough projectives P. We introduce the notion of supportτ-tilting subcategories of E. It is compatible with the existing definitions of supportτ-tilting modules (subcategories) in various context. It is also a generalization of tilting subcategories of exact categories. We show that there is a bijection between supportτ-tilting subcategories and certainτ-cotorsion pairs. Given a supportτ-tilting subcategory T , we find a subcategory E_T of E which is an exact category and T is a tilting subcategory of E_T . If E is Krull-Schmidt, we prove the cardinal |T| is equal to the number of isomorphism classes of indecomposable projectives Q such that Hom_{E}(Q, T)≠0. We also show a functorial version of Brenner-Butler’s theorem. This is a joint work with Jixin Pan and Yaohua Zhang.

报告人简介：

朱彬，清华大学数学科学系教授、博士生导师，1999年博士毕业于德国比勒菲尔德大学，研究方向为代数表示论。主持或完成多项国家自然科学基金项目，曾担任比利时FWO自然科学基金，以色列自然科学基金通信评委。研究成果发表于Trans. AMS.、J. Lond. Math. Soc.、Math. Z.、J. Algebra等杂志。