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DTSTART:20200329T030000
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DTSTAMP:20210515T020203Z
UID:1591876800@ist.ac.at
DTSTART:20200611T140000
DTEND:20200611T160000
DESCRIPTION:Speaker: Dimitri Wyss\nhosted by Tamas Hausel\nAbstract: Integr
ation with respect to the Haar measure over a non-archimedean local field
F shares many formal properties with integration over the reals while at t
he same time being closely related to the arithmetic and geometry over the
residue field of F. In the first part I will give an overview of the theo
ry and explain two classical applications\, namely rationality of Igusa's
local zeta functions and Batyrev's proof of the equality of Hodge numbers
for smooth projective birational Calabi-Yau varieties.In the second part I
explain joint work with Michael Groechenig and Paul Ziegler\, where we ap
ply these ideas to the moduli space of G-Higgs bundles. In quite general s
ituations we can relate p-adic volumes of Higgs spaces for Langlands-dual
groups\, from which we derive two results: the topological mirror symmetry
conjecture of Hausel-Thaddeus\, which relates Hodge numbers for SL_n and
PGL_n Higgs spaces\, and the geometric stabilization theorem for anisotrop
ic Hitchin fibers of NgĂ´. If time permits I will also discuss recent idea
s on how to effectively compute the p-adic volumes appearing in our argume
nt.
LOCATION: https://mathseminars.org/seminar/AGNTISTA\, IST Austria
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:P-adic integration\, geometry and Higgs bundles
URL:https://talks-calendar.app.ist.ac.at/events/2773
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