Geometric perspectives on categorical braid group actions

One of the many intriguing discoveries inspired by Kontsevich's homological mirror symmetry is the concept of spherical twists, introduced by Seidel and Thomas. These are autoequivalences described by a categorification of the classical Picard-Lefschetz formula for monodromy actions on homology.
More recently, it was proposed by Kapranov and Schechtman to interpret spherical twists within a (still hypothetical) theory of categorical analogs of perverse sheaves, so-called perverse schobers. In this talk, I will give an introduction to this circle of ideas, outline some recent progress on perverse schobers, and explain how they provide new structural insights on categorical braid group actions relevant for link homology theory.