BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Junliang Shen (Yale University) DTSTART:20240509T083000Z DTEND:20240509T093000Z DTSTAMP:20260422T161047Z UID:HKUST-AG/52 DESCRIPTION:Title: From abelian schemes to Hitchin systems: cohomology\, sheaves\, and alge braic cycles III\nby Junliang Shen (Yale University) as part of Algebr a and Geometry Seminar @ HKUST\n\nLecture held in Room 2408 (Lifts 17/18)\ , Academic Building\, HKUST.\n\nAbstract\nThis is a series of 3 talks\, wh ere we will focus on geometry and topology of abelian fibrations --- these are maps whose general fibers are complex tori but special fibers may be highly singular and complicated. The decomposition theorem of Beilinson\, Bernstein\, Deligne\, and Gabber (BBDG) provides powerful tools for studyi ng these maps\; Corti-Hanamura further conjectured that the sheaf-theoreti c BBDG decomposition is governed by algebraic cycles. In my talks\, I will explain how to find these algebraic cycles for certain geometries. I will start with the case of an abelian scheme (i.e.\, an abelian fibration wit hout singular fiber)\, where the desired cycles have been found by Beauvil le and Deninger-Murre more than 30 years ago. Then I will discuss the case with singular fibers. Our ultimate goal for this lecture series is to exp lain how to find the cycles for Hitchin’s integrable system. If time per mits\, I will discuss how/why these cycles can help us to understand vario us cohomological and sheaf-theoretic questions/conjectures for the Hitchin system. Based on joint work (in progress) with Davesh Maulik and Qizheng Yin.\n LOCATION:https://researchseminars.org/talk/HKUST-AG/52/ END:VEVENT END:VCALENDAR