Perverse sheaves, perverse schobers and physical "theories"

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.

Collection/Series: 
Event Type: 
Seminar
Speaker(s): 
Event Date: 
Mercredi, Février 27, 2019 - 14:00 to 15:30
Location: 
Time Room
Room #: 
294