Homological Mirror Symmetry - Yan Soibelman

Explore a lecture on Holomorphic Floer Theory (HFT), wall-crossing structures, and Chern-Simons theory presented by Yan Soibelman from Kansas State University. Delve into the mathematics behind Fukaya categories of complex symplectic manifolds and their relation to deformation quantization. Examine the generalized Riemann-Hilbert correspondence and its connection to Picard-Lefschetz wall-crossing formulas for exponential integrals. Discover how wall-crossing formulas and structures emerge from holomorphic Lagrangian subvarieties and their link to resurgence in Chern-Simons theory. Investigate the "Chern-Simons wall-crossing structure" through finite-dimensional geometry of K_2-Lagrangian subvarieties and a conjectured infinite-rank Hodge structure. Gain insights into the interplay between the "A-side" (Fukaya category) and "B-side" (deformation quantization) of complex symplectic manifolds in this advanced mathematical exploration.