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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.