| I will begin by reviewing the geometry of a cyclic cover branched in a divisor. I will then explain how it gives the first ever example of a non-split P^n-functor. Given a sphere or a complex projective space on a Lagrangian manifold Y, one can construct a certain natural symplectomorphism of Y called a Dehn twist. Spherical and P^n-functors are mirror symmetrical equivalents of this. These are functors between derived categories of algebraic varieties which induce natural autoequivalences known as spherical or P^n-twists. They arise naturally in many contexts related to moduli spaces or geometric representation theory. If there is time, I will also explain the connection with the notion of a perverse schober introduced recently by Kapranov and Schechtmann. This is a joint work with Rina Anno (Kansas). |