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Explore a lecture on stability structures in holomorphic Morse-Novikov theory delivered by Maxim Kontsevich from the Institut des Hautes Études Scientifiques and University of Miami. Delve into an elementary example illustrating the general program relating Floer theory for complex symplectic manifolds, quantization, and resurgence. Examine the space of morphisms between two specific branes in the cotangent bundle to a complex manifold, focusing on the zero section with a generic rank 1 local system and the graph of a closed holomorphic 1-form. Investigate how this case reduces to Morse-Novikov theory and sheaf theory, while highlighting the delicate analytic questions surrounding convergence. Gain insights into the potential generalization of these concepts to the almost-complex case.
