The flop-flop autoequivalence via spherical functors

The derived category of a scheme X is an algebraic object whose interest in geometry is beyond doubt. Among the various things one can be interested in about D(X), there are its symmetries, i.e its autoequivalences. The study of the autoequivalences of D(X) has attracted a lot of attention, and although in some cases this group is completely described, there is no "general" recipe to construct all the autoequivalences of D(X). A (conjectural) source of autoequivalences are flops. In this talk, I will discuss the so called "flop-flop" autoequivalence, and explain how it can be realised as the (inverse) spherical twist around a spherical functor.