Derived symplectic geometry and AKSZ topological field theories

Abstract: Derived algebraic geometry and derived symplectic geometry in the sense of Pantev-Toen-Vaquié-Vezzosi allows for a reinterpretation/analog of the classical AKSZ construction for certain $\sigma$-models. After recalling this procedure I will explain how it can be extended to give a fully extended oriented TFT in the sense of Lurie with values in a higher category whose objects are $n$-shifted symplectic derived stacks and (higher) morphisms are (higher) Lagrangian correspondences. It is given by taking mapping stacks with a fixed target building and describes ``semi-classical TFTs". This is joint work in progress with Damien Calaque and Rune Haugseng.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

Comments: Meeting Link Thursday 18 February, 12:00 - 13:00 (GMT) us02web.zoom.us/j/87160036709 Meeting ID: 871 6003 6709 Passcode: LAGOON

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

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