I will talk about two notions of dimension of a triangulated category. The first one is the classical Rouquier dimension, based on generation time with respect to a generator, while the second one is the more recent concept of Serre dimension, based on behavior of iterations of the Serre functor. I will propose ‘ideal’ properties of dimension that one would like to have, and compare them to properties of Rouquier and Serre dimension, both known and conjectural. Various examples of categories where dimension is known will be given and discussed.
This is based on joint work with Valery Lunts.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
