BIMSA > Algebra Learning Seminar Algebra Learning Seminar On the Serre dimension and stability conditions of triangulated categories
On the Serre dimension and stability conditions of triangulated categories
Organizer
Yu Qiu
Speaker
Suiqi Lu
Time
Monday, April 6, 2026 9:30 PM - 10:30 PM
Venue
Online
Online
Zoom 928 682 9093 (BIMSA)
Abstract
For autoequivalences of triangulated categories, Dimitrov–Haiden–Katzarkov–Kontsevich defined the notion of entropy motivated by the categorification of classical topological entropy, which is defined by the growth of generation-time with respect to a split-generator. They computed the entropy of the Serre functor in some cases, and Elagin–Lunts defined the upper Serre dimension and the lower Serre dimension as the growth of the entropy of the Serre functor. I will follow K. Kikuta, G. Ouchi and A. Takahashi's work to introduce the definition of the Serre dimension and relations between the Serre dimension and the global dimension of Bridgeland stability conditions due to Ikeda-Qiu. I will introduce the fundamental inequality between the upper Serre dimension and the infimum of the global dimensions, and introduce the conditions under which the equality holds for a fractional Calabi–Yau category. I will also introduce the study of the triangulated categories with low Serre dimension.