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SUMMARY:Symplectic pushforwards and Lagrangian classes - Hyeonjun Park\, K
 IAS
DTSTART:20251001T131500Z
DTEND:20251001T141500Z
UID:TALK235471@talks.cam.ac.uk
CONTACT:Dhruv Ranganathan
DESCRIPTION:Fundamental examples of symplectic varieties are moduli spaces
  of sheaves on K3 surfaces. This can be extended to higher-dimensional Cal
 abi-Yau varieties through the concept of shifted symplectic structures in 
 derived algebraic geometry. In the first half of the talk\, I will introdu
 ce a general operation of producing shifted symplectic stacks from given o
 nes. Basic examples like cotangent bundles\, critical loci\, and Hamiltoni
 an reduction can be understood as special cases of this operation. Moreove
 r\, this unification enables us to provide an etale local structure theore
 m for shifted symplectic Artin stacks.\nIn the second half of the talk\, I
  will provide an application to enumerative geometry. I will explain the c
 onstruction of Lagrangian classes for perverse sheaves in cohomological Do
 naldson-Thomas theory\, whose existence was conjectured by Joyce. As examp
 les\, I will explain how to construct the following structures from the La
 grangian classes: (1) cohomological field theories for gauged linear sigma
  models\; (2) cohomological Hall algebras for 3-Calabi-Yau categories\; (3
 ) relative Donaldson-Thomas invariants for Fano 4-folds with anti-canonica
 l divisors\; (4) refined surface counting invariants for Calabi-Yau 4-fold
 s. This is joint work in progress with Adeel Khan\, Tasuki Kinjo\, and Pav
 el Safronov.
LOCATION:CMS MR11
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