Topological Fukaya categories with coefficients

Abstract: Within an emerging approach to Fukaya categories via cohomology with categorical coefficients, I will outline a theory of a particularly nice class of nonconstant coefficient systems defined on Riemann surfaces. These are categorical analogues of perverse sheaves, called perverse schobers. We provide a definition of perverse schobers as categorical sheaves on a relative two-colored version of the unital Ran space of the surface. We explain how to describe perverse schobers locally in terms of a paracyclic upgrade of Waldhausen's relative Sconstruction applied to spherical functors. We conclude, time permitting, with some applications.