Perverse sheaves, perverse schobers and physical "theories"
APA
Kapranov, M. (2019). Perverse sheaves, perverse schobers and physical "theories". Perimeter Institute. https://pirsa.org/19020063
MLA
Kapranov, Mikhail. Perverse sheaves, perverse schobers and physical "theories". Perimeter Institute, Feb. 27, 2019, https://pirsa.org/19020063
BibTex
@misc{ pirsa_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}, year = {2019}, month = {feb}, note = {PIRSA:19020063 see, \url{https://pirsa.org}} }
University of Tokyo
Talk Type
Subject
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.