相对丛范畴短期课程
数学专题报告
报告题目(Title)：相对丛范畴短期课程
报告人(Speaker)：吴燚林（中国科学技术大学博士后）
地点(Place)：新主楼1220报告厅
时间(Time)：2024年9月19日、20日、23日、26日,15:20-16:20
邀请人(Inviter)：刘玉明
报告摘要
Cluster categories were introduced in 2006 by Buan-Marsh-Reineke-Reiten-Todorov to categorify acyclic cluster algebras without coefficients. Their construction was generalized by Amiot (2009) and Plamondon (2011) to arbitrary cluster algebras associated with quivers. A higher dimensional generalization is due to Guo (2011). Cluster algebras with coefficients are important since they appear in nature as coordinate algebras of varieties like Grassmannians, double Bruhat cells, unipotent cells, etc. The work of Geiss-Leclerc-Schröer often yields Frobenius exact categories which allow us to categorify such cluster algebras. In this lecture, we introduce the construction of relative cluster categories and Higgs categories which categorify cluster algebras with coefficients. This generalizes the construction of (higher) cluster categories by Claire Amiot and by Lingyan Guo to the relative context.
First talk: Relative Calabi-Yau structures
Second talk: Relative Calabi-Yau completions
Third talk: Cluster algebras and its categorification
Fourth talk: Relative cluster categories and Higgs categories
