Explore the connections between resurgence theory and analytic wall-crossing structures in this advanced mathematics lecture. Delve into the concept of Holomorphic Floer Theory, which originates from symplectic topology and complex symplectic manifolds. Examine the generalized Riemann-Hilbert correspondence, linking Fukaya categories with categories of holonomic deformation-quantization modules. Investigate how this correspondence relates to resurgence in perturbative expansions found in mathematics and mathematical physics. Study examples involving exponential integrals and WKB expansions of wave functions associated with quantum spectral curves. Gain insights into the simplest non-trivial case of Holomorphic Floer theory, focusing on pairs of complex Lagrangian submanifolds within complex symplectic manifolds.