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SUMMARY:Junliang Shen (MIT)
DTSTART:20201006T160000Z
DTEND:20201006T170000Z
DTSTAMP:20260423T021216Z
UID:ZAG/55
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/55/">Coh
 omology of the moduli of Higgs bundles and the Hausel-Thaddeus conjecture<
 /a>\nby Junliang Shen (MIT) as part of ZAG (Zoom Algebraic Geometry) semin
 ar\n\n\nAbstract\nWe describe the cohomological structure of the moduli sp
 ace of stable SL_n Higgs bundles on a curve following the topological mirr
 or symmetry conjecture of Hausel-Thaddeus. For the approach\, we establish
  a connection between:\n(a) the moduli space of twisted Higgs bundles by a
 n effective divisor of degree greater than 2g-2\, and\n(b) the moduli spac
 e of K_C-Higgs bundles\,\nusing vanishing cycle functors. This allows us t
 o apply Ngo's support theorem\, which has a simpler form in the case (a) (
 by Ngo\, Chaudouard-Laumon\, de Cataldo)\, to the case of (b) which concer
 ns hyper-Kähler geometries. In particular\, this gives a new proof of the
  Hausel-Thaddeus conjecture proven previously by Gröchenig-Wyss-Ziegler v
 ia p-adic integrations. Based on joint work with Davesh Maulik.\n
LOCATION:https://researchseminars.org/talk/ZAG/55/
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