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DTSTART:20200329T030000
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DTSTAMP:20260404T133037Z
UID:1602158400@ist.ac.at
DTSTART:20201008T140000
DTEND:20201008T153000
DESCRIPTION:Speaker: Mirko Mauri\nhosted by Tamas Hausel\nAbstract: Charact
 er varieties parametrise representations of the fundamental group of a cur
 ve. They are in general singular moduli spaces\, and for this reason it is
  customary to shift attention to smooth analogues\, called twisted charact
 er varieties. The P=W conjecture formulated by de Cataldo\, Hausel and Mig
 liorini posits a relation between the Hodge theory of twisted character va
 rieties and the geometry of some holomorphic Lagrangian fibrations. In a j
 oint work with Camilla Felisetti\, we explore P=W phenomena in the untwist
 ed case. We show that the P=W conjecture holds for character varieties whi
 ch admit a symplectic resolution\, namely in genus 1 and arbitrary rank an
 d in genus 2 and rank 2. This involves a careful study of alterations of t
 hese character varieties. If time permits\, I will discuss new numerical e
 vidence of P=W phenomena in higher genus\, when no symplectic resolution e
 xists.
LOCATION:https://mathseminars.org/seminar/AGNTISTA\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Mirko Mauri: P=W conjectures for character varieties with symplecti
 c resolution
URL:https://talks-calendar.ista.ac.at/events/2867
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