Perverse Sheaves and Resurgence in Borel Summation

Explore the intersection of resurgence theory and perverse sheaves in this advanced mathematics lecture. Delve into how the Borel summation procedure translates irregular behavior governed by asymptotic series and Stokes phenomena into multivalued functions in the Borel plane. Examine a proposed framework for resurgence based on perverse sheaves that are algebras with respect to additive convolution. Investigate the singularity structure of perverse sheaves on C, focusing on vanishing cycles and transport maps. Learn how alien derivatives adapt to this context and discover how Fourier transforms of convolution algebras lead to tensor product algebras with Stokes matrices as algebra automorphisms. Gain insights into ongoing joint research with Y. Soibelman in this cutting-edge exploration of mathematical concepts.