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SUMMARY:Dimitri Wyss (L'Ecole polytechnique fédérale de Lausanne (EPFL))
DTSTART:20200611T120000Z
DTEND:20200611T140000Z
DTSTAMP:20260423T041353Z
UID:AGNTISTA/9
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AGNTISTA/9/"
 >P-adic integration\, geometry and Higgs bundles</a>\nby Dimitri Wyss (L'E
 cole polytechnique fédérale de Lausanne (EPFL)) as part of Algebraic Geo
 metry and Number Theory seminar - ISTA\n\n\nAbstract\nIntegration with res
 pect to the Haar measure over a non-archimedean local field F shares many 
 formal properties with integration over the reals while at the same time b
 eing closely related to the arithmetic and geometry over the residue field
  of F. In the first part I will give an overview of the theory and explain
  two classical applications\, namely rationality of Igusa's local zeta fun
 ctions and Batyrev's proof of the equality of Hodge numbers for smooth pro
 jective birational Calabi-Yau varieties.\n\nIn the second part I explain j
 oint work with Michael Groechenig and Paul Ziegler\, where we apply these 
 ideas to the moduli space of G-Higgs bundles. In quite general situations 
 we can relate p-adic volumes of Higgs spaces for Langlands-dual groups\, f
 rom which we derive two results: the topological mirror symmetry conjectur
 e of Hausel-Thaddeus\, which relates Hodge numbers for SL_n and PGL_n Higg
 s spaces\, and the geometric stabilization theorem for anisotropic Hitchin
  fibers of Ngô. If time permits I will also discuss recent ideas on how t
 o effectively compute the p-adic volumes appearing in our argument.\n
LOCATION:https://researchseminars.org/talk/AGNTISTA/9/
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