BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mirko Mauri (Max Planck Institute\, Bonn) DTSTART:20201008T120000Z DTEND:20201008T133000Z DTSTAMP:20260423T005758Z UID:AGNTISTA/12 DESCRIPTION:Title: P=W conjectures for character varieties with symplectic resolution\n by Mirko Mauri (Max Planck Institute\, Bonn) as part of Algebraic Geometry and Number Theory seminar - ISTA\n\n\nAbstract\nCharacter varieties param etrise representations of the fundamental group of a curve. They are in ge neral singular moduli spaces\, and for this reason it is customary to shif t attention to smooth analogues\, called twisted character varieties. The P=W conjecture formulated by de Cataldo\, Hausel and Migliorini posits a r elation between the Hodge theory of twisted character varieties and the ge ometry of some holomorphic Lagrangian fibrations. In a joint work with Cam illa Felisetti\, we explore P=W phenomena in the untwisted case. We show t hat the P=W conjecture holds for character varieties which admit a symplec tic resolution\, namely in genus 1 and arbitrary rank and in genus 2 and r ank 2. This involves a careful study of alterations of these character var ieties. If time permits\, I will discuss new numerical evidence of P=W phe nomena in higher genus\, when no symplectic resolution exists.\n LOCATION:https://researchseminars.org/talk/AGNTISTA/12/ END:VEVENT END:VCALENDAR