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PIRSA:19020063

Perverse sheaves, perverse schobers and physical "theories"

APA

Kapranov, M. (2019). Perverse sheaves, perverse schobers and physical "theories". Perimeter Institute for Theoretical Physics. https://pirsa.org/19020063

Mikhail Kapranov University of Tokyo

Talk numberPIRSA:19020063
Talk Type Conference

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.