Exponential integrals, Holomorphic Floer theory and resurgence

Abstract: Holomorphic Floer theory is a joint project with Maxim Kontsevich, which is devoted to various aspects of the Floer theory in the framework of complex symplectic manifolds.

In my talk I will consider an important special case of the general story. Exponential integrals in finite and infinite dimension can be thought of generalization of the theory of periods (i.e variations of Hodge structure). In particular, there are comparison isomorphisms between Betti and de Rham cohomology in the exponential setting. These isomorphisms are corollaries of categorical equivalences which are incarnations of our generalized Riemann-Hilbert correspondence for complex symplectic manifolds.

Furthermore, fomal series which appear e.g. in the stationary phase method or Feynman expansions (in infinite dimensions) are Borel re-summable (resurgent). If time permits I will explain the underlying mathematical structure which we call analytic wall-crossing structure. From the perspective of Holomorphic Floer theory it is related to the estimates for the number of pseudo-holomorphic discs with boundaries on two given complex Lagrangian submanifolds.

algebraic geometry

Audience: researchers in the topic

UBC Vancouver Algebraic Geometry Seminar

Series comments: Recordings and slides are available on the seminar webpage:

wiki.math.ubc.ca/mathbook/alggeom-seminar/Main_Page