Gustavo Jasso (Bonn), Spherical objects in higher Auslander-Reiten theory

Abstract:

Spherical objects were introduced by Seidel and Thomas in 2001, motivated by Kontsevich's Homological Mirror Symmetry Conjecture. In this talk I will explain how to construct a family of triangulated categories T(d,m) containing dm-spherical objects.From the viewpoint of Iyama's higher Auslander-Reiten theory, these categories should be thought of as higher dimensional analogues of the triangulated category generated by an m-spherical object. This is a report on joint work in progress with Julian Külshammer.