Sheaves of categories over topological and coaffine stacks

Abstract: Starting from any sufficiently nice topological space X, one can produce two different (derived) stacks defined over a field k of characteristic 0: the Betti stack X_B, which bears information on the underlying homotopy type of X, and the coaffine stack cSpec(C*(X; k)) on the commutative algebra C*(X; k) of k-valued singular cochains on X, which behaves as the affinization of the Betti stack X_B. In this talk, I shall apply the technical machinery of sheaves of (∞-)categories on derived stacks as developed in Gaitsgory’s work to the case of Betti stacks and their associated coaffine stacks. We shall see how sheaves of categories on X_B are intimately related to categorified local systems over the original space X and to homotopy-coherent actions of topological groups on k-linear ∞-categories. At the very end, I shall briefly describe how sheaves of categories on X_B and on cSpec(C*(X; k)) interact, and how such interaction can be interpreted as an instance of higher Koszul duality. This talk is based on upcoming joint work with J. Pascaleff and N. Sibilla.See abstract under 'Paper link' below.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

Comments: Live stream: uni-koeln.zoom.us/j/91875528987?pwd=US8wdjNrWjl5dXNQSVRzREhoRE1PUT09

Meeting ID: 918 7552 8987 Password: LAGOON

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