SIMIS Seminar on Derived and Noncommutative Geometry: Introduction to Shifted Symplectic structure and Lagrangian structure

Speaker: Yingdi Qin (SIMIS)

Abstract: In classical geometry, a symplectic structure on a manifold is a non-degenerate closed 2-form. And a submanifold Y is called Lagrangian if the pull back of the closed 2-form is trivial and the induced bundle map from TY to TY is an isomorphism. In derived geometry, tangent bundles are replaced by tangent complexes. A (derived) symplectic structure is a non-degenerated 2-form together with some homotopy data assuring the closedness. And a Lagrangian condition is some homotopy data making the pullback of the 2-form exact and induces the quasi-isomorphism from TY to TY. I will describe the example that a Poisson structure is equivalent to an 1-shifted nil-Lagrangian structure.

Time: 16:00~19:00 (with break for tea), Monday, Oct. 21, 2024

Location: Room 1410, Block A, No. 657 Songhu Road, Yangpu District, Shanghai

en_USEnglish
Scroll to Top