Летняя математическая школа "Алгебра и геометрия"

Symplectic structures on moduli spaces and quantization

Ник Розенблюм (Chicago)

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Резюме

Many moduli problems of interest, such as moduli spaces of local systems, come equipped with a natural symplectic structure. The theory of shifted symplectic and Poisson structures 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. In these lectures we will give an overview of derived geometry and the theory of shifted symplectic structures with an emphasis on applications to moduli problems.

No prior experience with derived algebraic geometry will be assumed, but familiarity with homotopical algebra will be helpful.