QM Research Seminar: Complexes of stable infinity-categories and perverse schobers

Speaker: Merlin Christ (Institut de mathématiques de Jussieu – Paris Rive Gauche)


Abstract:

A complex of stable infinity-categories is a categorification of a chain complex, meaning a sequence of stable infinity-categories together with a differential that squares to the zero functor. To produce examples of such categorical complexes we introduce a categorification of the totalization construction, which produces a categorical complex from a categorical multi-complex, such as a commuting cube of stable infinity-categories. We will then explain how categorified perverse sheaves, also known as perverse schobers, on C^n (with a certain stratification) can be described in terms of categorical cubes and categorical complexes of spherical functors. We will also see what categorical totalization means in this case geometrically. This talk is based on joint work with T. Dyckerhoff and T. Walde.