Graded sheaves and categorification of q
数学专题报告
报告题目(Title)：Graded sheaves and categorification of q
报告人(Speaker)：李鹏辉（清华大学）
地点(Place)：后主楼1220
时间(Time)：2024年10月18日 13:00-14:00
邀请人(Inviter)：田垠
报告摘要
I will present joint work with Quoc P. Ho on our theory of graded sheaves, which offers a uniform construction of "mixed versions" or "graded lifts" in the sense of Beilinson–Ginzburg–Soergel applicable to arbitrary Artin stacks. As a straightforward reinterpretation of classical results, this framework allows for the categorification of many quantum algebras, including Hecke algebras and positive quantum groups, through graded sheaves.In a new application, we introduce a graded version of Lusztig's character sheaves and utilize it to prove a conjecture by Gorsky, Negut, and Rasmussen,which establishes a connection between the HOMFLY homology of knots and links and the cohomology of coherent sheaves on Hilbert schemes.
