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SUMMARY:Penghui Li (Tsinghua University)
DTSTART:20230927T070000Z
DTEND:20230927T083000Z
DTSTAMP:20260422T155945Z
UID:HKUST-AG/22
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/HKUST-AG/22/
 ">Graded character sheaves\, HOMFLY-PT homology\, and Hilbert schemes of p
 oints on $\\mathbb{C}^2$</a>\nby Penghui Li (Tsinghua University) as part 
 of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 4475.\n\nA
 bstract\nUsing a geometric argument building on our new theory of graded s
 heaves\, we compute the categorical trace and Drinfel'd center of the (gra
 ded) finite Hecke category $\\mathsf{H}_W$ 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 categori
 cal trace to the category of 2-periodic coherent sheaves on the Hilbert s
 chemes of points on $\\mathbb{C}^2$ (equivariant with respect to the na
 tural $\\mathbb{C}^* \\times \\mathbb{C}^*$ action)\, yielding a proof o
 f a conjecture of Gorsky-Negut-Rasmussen which relates HOMFLY-PT link homo
 logy and the spaces of global sections of certain coherent sheaves on Hil
 bert schemes. As an important computational input\, we also establish a co
 njecture of Gorsky-Hogancamp-Wedrich on the formality of the Hochschild ho
 mology of $\\mathsf{H}_W$. This is a joint work with Quoc P. Ho.\n
LOCATION:https://researchseminars.org/talk/HKUST-AG/22/
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