BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Quoc P. Ho (Hong Kong University of Science and Technology) DTSTART:20220317T120000Z DTEND:20220317T140000Z DTSTAMP:20260423T041351Z UID:AGNTISTA/55 DESCRIPTION:Title: Revisiting mixed geometry\nby Quoc P. Ho (Hong Kong University of Sc ience and Technology) as part of Algebraic Geometry and Number Theory semi nar - ISTA\n\n\nAbstract\nI will present joint work with Penghui Li on our theory of graded sheaves on Artin stacks. Our sheaf theory comes with a s ix-functor formalism\, a perverse t-structure in the sense of Beilinson--B ernstein--Deligne--Gabber\, and a weight (or co-t-)structure in the sense of Bondarko and Pauksztello\, all compatible\, in a precise sense\, with t he six-functor formalism\, perverse t-structures\, and Frobenius weights o n ell-adic sheaves. The theory of graded sheaves has a natural interpretat ion in terms of mixed geometry à la Beilinson--Ginzburg--Soergel and prov ides a uniform construction thereof. In particular\, it provides a general construction of graded lifts of many categories arising in geometric repr esentation theory and categorified knot invariants. Historically\, constru ctions of graded lifts were done on a case-by-case basis and were technica lly subtle\, due to Frobenius' non-semisimplicity. Our construction sidest eps this issue by semi-simplifying the Frobenius action itself. As an appl ication\, I will conclude the talk by showing that the category of constru ctible B-equivariant graded sheaves on the flag variety G/B is a geometriz ation of the DG-category of bounded chain complexes of Soergel bimodules.\ n LOCATION:https://researchseminars.org/talk/AGNTISTA/55/ END:VEVENT END:VCALENDAR