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SUMMARY:Andrew Harder (Lehigh University)
DTSTART:20201217T160000Z
DTEND:20201217T170000Z
DTSTAMP:20260423T021358Z
UID:ZAG/78
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ZAG/78/">Log
  symplectic pairs and mixed Hodge structures</a>\nby Andrew Harder (Lehigh
  University) as part of ZAG (Zoom Algebraic Geometry) seminar\n\n\nAbstrac
 t\nA log symplectic pair is a pair (X\,Y) consisting of a smooth projectiv
 e variety X and a divisor Y in X so that there is a non-degenerate log 2-f
 orm on X with poles along Y. I will discuss the relationship between log s
 ymplectic pairs and degenerations of hyperkaehler varieties\, and how this
  naturally leads to a class of log symplectic pairs called log symplectic 
 pairs of "pure weight". I will talk about common properties of cohomology 
 rings of log symplectic pairs of pure weight and type III degenerations of
  hyperkaehler varieties\, in particular\, the fact that both have the curi
 ous hard Lefschetz' (CHL) property discovered by Hausel and Rodriguez-Vill
 egas. Finally I will discuss partial results towards proving that in both 
 of these cases\, the CHL property is a consequence of P=W type results. Pa
 rt of this is based on work with Li\, Shen\, and Yin.\n
LOCATION:https://researchseminars.org/talk/ZAG/78/
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