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Presented By: Algebraic Geometry Seminar - Department of Mathematics

Algebraic Geometry Seminar (note special day): Shifted symplectic pushforwards

Hyeonjun Park (Korea Institute for Advanced Study)

Fundamental examples of symplectic varieties are moduli spaces of sheaves on K3 surfaces. This can be extended to higher-dimensional Calabi-Yau varieties through the concept of shifted symplectic structures in derived algebraic geometry. In this talk, I will introduce a general operation of producing shifted symplectic stacks from given ones. Basic examples like cotangent bundles, critical loci, and Hamiltonian reduction can be understood as special cases of this operation. Moreover, this unification enables us to provide an etale local structure theorem for shifted symplectic Artin stacks. I will briefly explain some applications to Donaldson-Thomas theory of Calabi-Yau 3-folds and 4-folds.

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