报告题目：Finitistic dimension of triangulated categories

主讲人：陈红星 教授（首都师范大学）

摘要：In the representation theory of algebras, finitistic dimension and related concepts are ubiquitous, and it is from there that we derive our inspiration. In this talk, we first recall several different ways of defining finitistic dimension for triangulated categories. In some cases, these notions were only defined for specific classes of triangulated categories, and we then extend these notions to general triangulated categories. However, to give a categorical obstruction to the existence of bounded t-structures on a triangulated category, we will introduce a new notion of finitistic dimension of triangulated categories and establish the finiteness of finitistic dimension (at classical generators) for several classes of triangulated categories, such as a triangulated category with an algebraic t-structure or with a strong generator, and the derived category of perfect complexes over a nice scheme. This talk is based on a part of joint work with Rudradip Biswas, Chris J. Parker, Kabeer Manali Rahul and Junhua Zheng.

报告时间：2024年11月16日上午10:30 - 11:20

报告地点：数学科学学院301室

报告人简介：陈红星，首都师范大学数学科学学院教授、德国洪堡学者。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，作为主要成员参与两项国家自然科学基金重点项目和一项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，在经典同调猜想（如Nakayama猜想和Tachikawa第二猜想）、导出范畴、无限维倾斜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，并系统建立了无限维倾斜模的导出粘合理论。研究成果发表于Compos. Math., Proc. Lond. Math. Soc., Trans. AMS等国际数学杂志。