| Speaker: | Penghui Li (Tsinghua University) |
|---|---|
| Title: | Graded character sheaves, HOMFLY-PT homology, and Hilbert schemes of points on C^2 |
| Date (JST): | Tue, Aug 29, 2023, 15:30 - 17:00 |
| Place: | Seminar Room A |
| Abstract: |
Using a geometric argument building on our new theory of graded sheaves, we compute the categorical trace and Drinfel'd center of the (graded) finite Hecke category H_W in terms of the category of (graded) unipotent character sheaves, upgrading results of Ben-Zvi-Nadler and Bezrukavninov-Finkelberg-Ostrik. In type A, we relate the categorical trace to the category of 2-periodic coherent sheaves on the Hilbert schemes of points on C^2 (equivariant with respect to the natural C*×C* action), yielding a proof of a conjecture of Gorsky-Negut-Rasmussen which relates HOMFLY-PT link homology and the spaces of global sections of certain coherent sheaves on Hilbert schemes. As an important computational input, we also establish a conjecture of Gorsky-Hogancamp-Wedrich on the formality of the Hochschild homology of H_W. It is a joint work with Quoc Ho. |
| Remarks: | Seminar Room A + Zoom |
