PIRSA:19020063 Conference Mathematical physics

DOI10.48660/19020063

Conference/School: Cohomological Hall Algebras in Mathematics and Physics

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

Kapranov, Mikhail. Perverse sheaves, perverse schobers and physical "theories". Perimeter Institute, Feb. 27, 2019, https://pirsa.org/19020063 

@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}}
}

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.

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