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SUMMARY:Curious Hard Lefschetz [MPIM]
DTSTART:20260601T130000Z
DTEND:20260601T150000Z
DTSTAMP:20260716T205100Z
UID:indico-event-1356@math-events.uni-bonn.de
DESCRIPTION:Speakers: Sasha Minets (MPIM)\n\nThe Unterseminar \nThe cohom
 ology of a smooth complex projective variety $X$ satisfies Poincaré duali
 ty\, which can be reformulated by saying that the Poincaré polynomial of 
 $X$ is palindromic. A stronger statement\, called Hard Lefschetz theorem\,
  is that $H^*(X)$ is naturally an $sl2$-module.In 2006\, Hausel and Rodrig
 uez-Villegas computed the number of $F_q$-points for some character variet
 ies (which are not projective)\, and observed that the resulting polynomia
 ls are palindromic. They suggested that this symmetry is also induced by a
 n $sl2$-action\, and dubbed this curious Hard Lefschetz conjecture. It is 
 by now a theorem\, proved in a couple of ways. I will start by going throu
 gh some very explicit examples\, then explain some of the ideas that go in
 to the proofs\, and if time permits gesture at what this theorem might be 
 telling us.  \n\nhttps://math-events.uni-bonn.de/event/1356/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1356/
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