Resurgent Perverse Sheaves and Topological Resurgence Theory
Explore the topological counterpart of resurgence theory in this advanced mathematics lecture. Delve into the world of perverse sheaves and their connection to regular holonomic D-modules, examining how they relate to multivalued functions. Investigate the application of additive convolution as a key tool in J. Ecalle's theory of resurgence. Learn about ongoing research that proposes a topological approach to resurgence theory using perverse sheaves on the complex plane, which function as algebras with respect to middle additive convolution. Discover how these sheaves typically possess infinitely many singular points. Gain insights into the localization of cohomological Hall algebra in a 3-Calabi-Yau situation to a "resurgent perverse sheaf". This talk, presented by Mikhail Kapranov from IPMU, is based on joint work with Y. Soibelman and offers a deep dive into cutting-edge mathematical concepts at the intersection of topology, algebra, and complex analysis.