Appears in collection : Algebraic Analysis in honor of Masaki Kashiwara's 70th birthday

Perverse schobers and conjectural categorical analogs of perverse sheaves, where vector spaces are replaced by triangulated categories. The talk will present a natural definition of such object for the case when the base space is a Riemann surface. The construction is based on a certain analog of the exit path category of the Ran space. Joint work with T. Dyckerhoff, V. Schechtman and Y. Soibelman.