Perverse Schobers on surfaces and Fukaya categories with coefficients

Perverse Schobers are conjectural categorical analogs of
perverse sheaves. The talk will present a precise definition of a
perverse Schober on an oriented surface and a construction of a
"global" category associated with such an object. This category
can be seen as the topological Fukaya category but with nontrivial
coefficients data provided by the perverse Schober. The talk is
based on joint work with T. Dyckerhoff, V. Schechtman and Y.
Soibelman.