Holomorphic Floer Theory, Quantum Wave Functions and Resurgence

Explore a comprehensive lecture on Holomorphic Floer Theory, Quantum Wave Functions, and Resurgence delivered by Yan Soibelman from Kansas State University. Delve into the interpretation of finite-dimensional exponential integrals over real cycles in affine complex algebraic varieties, examining their relation to exponential periods and the isomorphism between twisted versions of de Rham and Betti cohomology. Investigate the upgrade of this relation in Holomorphic Floer Theory, focusing on the equivalence between the Fukaya category of the cotangent bundle and the category of holonomic DQ-modules. Analyze the analytic behavior of stationary phase expansion in exponential integrals, exploring its connection to the moduli space of pseudo-holomorphic discs and the concept of resurgence. Discover the extension of these concepts to infinite-dimensional exponential integrals, including complexified Chern-Simons theory, and examine the emerging mathematical structure of quantum wave functions in this context.