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Physically Inspired Mathematics Seminar – Mikhail Kapranov (IMPU)
October 30, 2023 @ 4:00 pm - 5:00 pm
Title: Perverse sheaves and resurgence.
Abstract: Perverse sheaves provide a topological counterpart of regular holonomic D-modules, whose solutions are multivalued functions of certain restricted type. Now, much more general multivalued functions (on the complex plane C) have been studied in J. Ecalle’s theory of resurgence using, as one of the main tools, additive convolution of analytic functions.
The talk, based on joint work in progress with Y. Soibelman, will propose a topological counterpart to the theory of resurgence based on perverse sheaves on C which are algebras with respect to (middle) additive convolutions. Such sheaves typically have infinitely many singular points. In particular, we will argue that the cohomological Hall algebra in a 3-Calabi-Yau situation localizes to such a “resurgent perverse sheaf”.