BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Junliang Shen (Yale University) DTSTART:20240508T083000Z DTEND:20240508T093000Z DTSTAMP:20260422T161057Z UID:HKUST-AG/51 DESCRIPTION:Title: From abelian schemes to Hitchin systems: cohomology\, sheaves\, and alge braic cycles II\nby Junliang Shen (Yale University) as part of Algebra 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\, whe re we will focus on geometry and topology of abelian fibrations --- these are maps whose general fibers are complex tori but special fibers may be h ighly singular and complicated. The decomposition theorem of Beilinson\, B ernstein\, Deligne\, and Gabber (BBDG) provides powerful tools for studyin g these maps\; Corti-Hanamura further conjectured that the sheaf-theoretic 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 with out singular fiber)\, where the desired cycles have been found by Beauvill e 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 expl ain how to find the cycles for Hitchin’s integrable system. If time perm its\, I will discuss how/why these cycles can help us to understand variou s cohomological and sheaf-theoretic questions/conjectures for the Hitchin system. Based on joint work (in progress) with Davesh Maulik and Qizheng Y in.\n LOCATION:https://researchseminars.org/talk/HKUST-AG/51/ END:VEVENT END:VCALENDAR