Perverse sheaves, perverse schobers and physical "theories"

          @misc{ scivideos_PIRSA:19020063,
            doi = {10.48660/19020063},
            url = {https://pirsa.org/19020063},
            author = {Kapranov, Mikhail},
            keywords = {Mathematical physics},
            language = {en},
            title = {Perverse sheaves, perverse schobers and  physical "theories"},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {feb},
            note = {PIRSA:19020063 see, \url{https://scivideos.org/index.php/pirsa/19020063}}
          }
          

Abstract

The mathematical concept of sheaves is a tool for > describing global structures via local data. Its generalization, the > concept of perverse sheaves, which appeared originally in the study of > linear PDE, turned out to be remarkably useful in many diverse areas > of mathematics. I will review these concepts as well as a more recent conjectural categorical generalization, called perverse schobers. > One reason for the interest in such structures is the remarkable > parallelism between: > > (1) The purely mathematical classification theory of perverse sheaves > on a complex plane with several singular points > (Gelfand-MacPherson-Vilonen). > > (2) The "infrared" analysis of > 2d supersymmetric theories (Gaiotto-Moore-Witten). > > I will explain this parallelism which suggests that the infrared > analysis should be formulated in terms of a perverse schober. This is > based on work in progress with Y. Soibelman and L. Soukhanov.