Title: Spherical functors
Speaker: Rina Anno
Speaker Info: Chicago
Brief Description:
Special Note:
Abstract:
Spherical objects are objects of a (Serre) triangulated category whose Ext groups are isomorphic to the cohomology groups of a sphere. The most basic example of a spherical object coming from the algebraic geometry is a structure sheaf of a (-2)-curve on a smooth surface. The notion of a spherical functor generalizes this to functors from some category into our category (i.e. instead of an object we want to consider a subcategory, and the best notion of a subcategory of a category C is a category with a functor into C). I will explain how spherical functors produce autoequivalences of the triangulated category, and describe the Khovanov and Thomas' braid group action on the derived category of coherent sheaves on the cotangent bundle to the flag variety.Date: Thursday, January 20, 2011