BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Dougal Davis (University of Melbourne) DTSTART:20231009T070000Z DTEND:20231009T083000Z DTSTAMP:20260422T161057Z UID:HKUST-AG/17 DESCRIPTION:Title: Unitary representations of real groups and localisation theory for Hodge modules\nby Dougal Davis (University of Melbourne) as part of Algebra and Geometry Seminar @ HKUST\n\nLecture held in Room 5560.\n\nAbstract\nI will explain recent joint work with Kari Vilonen\, in which we prove a co njecture of Schmid and Vilonen linking mixed Hodge modules on flag varieti es to unitary representations of real reductive Lie groups. The main idea behind our work is to upgrade Beilinson-Bernstein localisation from D-modu les to mixed Hodge modules. When it applies\, this endows everything in si ght with a canonical filtration\, the Hodge filtration\, which we prove ha s some extremely nice properties\, such as cohomology vanishing and global generation. In the context of real groups\, we also prove that the Hodge filtration “sees” exactly which representations are unitary. We hope t hat this will lead to new progress on the very old problem of determining the unitary dual of a real group.\n LOCATION:https://researchseminars.org/talk/HKUST-AG/17/ END:VEVENT END:VCALENDAR