Abstract:

Holomorphic Floer Theory is the name of our joint project (in fact a program) with Maxim Kontsevich.It is devoted to various aspects of the Floer theory of complex symplectic manifolds.Among applications of our approach there are generalizations of the Riemann-Hilbert correspondence and non-abelian Hodge theory, relation of the Fukaya categories with periodic monopoles,conceptual understanding of coisotropic branes in physics and more.

In my talk I am going to discuss an application of Holomorphic Floer Theory to exponential integrals in finite and infinite dimensions.Geometrically many properties of these integrals are controlled by the Floer Theory of a pair of complex Lagrangian submanifolds sitting in a complex symplectic manifold.I plan to discuss the wall-crossing formulas for exponential integrals including the underlying abstract structure known as wall-crossing structure.In these terms one can explain the resurgent properties of a priori divergent series arising from exponential integrals.If time permits I am going to discuss an application of our approach to the Chern-Simons theory as well as its relation to the theory of quantum wave functions and to the more speculative Hodge theory of infinite rank.

Bio:

Yan Soibelman has done an important work in many areas of mathematics and mathematical physics such as quantum groups, Mirror Symmetry, homological algebra, representation theory, theory of Donaldson-Thomas invariants and more (seehttps://en.wikipedia.org/wiki/Yan_Soibelman).As a gradute student he solved the famous problem of Polya of finding the asymptotic expansion of the capacity of a condenser with respect to the small parameter given by the distance between plates.He developed the theory of representations of quantized function algebras in the 80's and based on that he introduced the notion of quantum Weyl group in 1990. In the long collaboration with Maxim Kontsevich he proved the famous Deligne's conjecture in 1998, proposed the idea about the relation of Mirror Symmetry with non-archimedean geometry and tropical geometry in 2000 and discovered a new type of wall-crossing formulas in Donaldson-Thomas theory and gauge theory in 2008.Soibelman was an invited professor at many famous reserch centers from all over the world, including Harvard, MIT, Institute for Adavanced Study in Princeton (USA), Newton Institute in Cambridge (UK), Max-Planck Institute in Bonn (Germany),  RIMS in Kyoto (Japan), and IHES in Bures-sur-Yvette (France).For many years he holds a Distinguished Visiting Research Chair position at the Perimeter Institute for Theoretical Physics in Waterloo (Canada).Currently he is a Distinguished University Professor at Kansas State University.

Slides：

 HFT and exp int.pdf

Video：

http://archive.ymsc.tsinghua.edu.cn/pacm_lecture?html=Holomorphic_Floer_Theory_and_exponential_integrals.html