中科院数学与系统科学研究院
数学研究所
学术报告
表示论研讨班
报告人：陈红星 教授 （首都师范大学）
时间：2024.01.16（星期二）上午9：30--10：30
地点：思源楼S817
题目：Bounded $t$-structures, finitistic dimensions and singularity categories of triangulated categories
摘要：In this talk, we establish some very general results about the existence of bounded $t$-structures on (not necessarily algebraic or topological) triangulated categories and the invariance of triangulated categories under completion. Our general treatment, when specialised to the case of noetherian schemes, immediately gives us Neeman's theorem on regularity (a major generalization of a conjecture by Antieau, Gepner and Heller) as an application and significantly generalizes another remarkable theorem by Neeman about the equivalence of bounded $t$-structures on bounded derived categories of coherent sheaves. When specialised to other cases like (not necessarily commutative) rings, nonpositive DG-rings, connective ring spectra, triangulated categories without models, etc., we get many other applications. All of these results convey that the singularity category, in our sense, is an obstruction to the existence of bounded $t$-structures. This reports a joint work with Rudradip Biswas, Chris Parker, Kabeer Manali Rahul and Junhua Zheng.
==================================
报告人：胡维 教授（北京师范大学）
时间：2024.1.16 (星期二) 上午10：40--11：40
地点：思源楼S817
题目：Moving vectors and weight spaces of highest weight modules
摘要：Recently, Yanbo Li and Xiangyu Qi introduced a new invariant of blocks of cyclotomic Hecke algebras to classify representation-finite blocks. In this talk, we define a vector for each weight space of irreducible highest weight modules for affine Kac-Moody algebra of type A. An interesting property of this vector is that the weight space is non-zero precisely when the vector is a vector of non-negative integers, in this case, it is exactly the moving vector of the corresponding cyclotomic Hecke algebra block via categorification. This is based on an ongoing work with Yanbo Li and Xiangyu Qi.
附件：