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Homological Mirror Symmetry

Wednesday, May 3, 2017 - 3:30pm

Nick Rozenblyum

University of Chicago

Location

University of Pennsylvania

DRL 4N30


Many moduli problems of interest, such as moduli spaces of local systems, come equipped
with a natural symplectic structure. The theory of shifted symplectic structures introduced by Pantev,
Toen, Vezzosi, and Vaquie is a vast generalization of algebraic symplectic geometry which provides a natural
framework for studying these symplectic structures. In addition to being a natural setting for the BV
approach to Feynman integration, this theory provides a robust framework for various counting problems in
geometry and topology, such as the theory of Donaldson-Thomas invariants and its generalizations. I
will describe a geometric approach to quantizations of shifted symplectic structures as well as several
applications.

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