Date: Thursday 29th November 2012
Speaker: Timothy Logvinenko (Warwick)
Title: Spherical DG-functors
Abstract: Seidel-Thomas twists are autoequivalences of the derived category D(X) of an algebraic variety X. They are the mirror symmetry analogues of Dehn twists along Lagrangian spheres on a symplectic manifold. Given an object E in D(X) with numerical properties of such a sphere, Seidel and Thomas defined the spherical twist of D(E) along E, proved it to be an autoequivalence and gave braiding criteria for several such twists.
It was long understood that all of the above should generalise to the notion of the twist along a spherical functor into D(X). In full generality this was long obstructed by some well-known imperfections of working with triangulated categories. In this talk, I present joint work with Rina Anno, where we fix this by working with the standard DG-enhancement of D(X). We define the notion of a spherical DG-functor and give the braiding criteria for twists along such functors.http://www.maths.ed.ac.uk/cheltsov/seminar/