BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Junliang Shen (Yale University) DTSTART:20240507T083000Z DTEND:20240507T093000Z DTSTAMP:20260422T161057Z UID:HKUST-AG/50 DESCRIPTION:Title: From abelian schemes to Hitchin systems: cohomology\, sheaves\, and alge braic cycles I\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\, wher e we will focus on geometry and topology of abelian fibrations --- these a re maps whose general fibers are complex tori but special fibers may be hi ghly singular and complicated. The decomposition theorem of Beilinson\, Be rnstein\, Deligne\, and Gabber (BBDG) provides powerful tools for studying these maps\; Corti-Hanamura further conjectured that the sheaf-theoretic BBDG decomposition is governed by algebraic cycles. In my talks\, I will e xplain how to find these algebraic cycles for certain geometries. I will s tart with the case of an abelian scheme (i.e.\, an abelian fibration witho ut singular fiber)\, where the desired cycles have been found by Beauville and Deninger-Murre more than 30 years ago. Then I will discuss the case w ith singular fibers. Our ultimate goal for this lecture series is to expla in how to find the cycles for Hitchin’s integrable system. If time permi ts\, I will discuss how/why these cycles can help us to understand various cohomological and sheaf-theoretic questions/conjectures for the Hitchin s ystem. Based on joint work (in progress) with Davesh Maulik and Qizheng Yi n.\n LOCATION:https://researchseminars.org/talk/HKUST-AG/50/ END:VEVENT END:VCALENDAR