Alessio Cipriani, University of Verona

Title: Highest weight categories via stability conditions.

Abstract: 

Highest weight categories were introduced by Cline Parshall and Scott in 1988. These categories satisfy nice properties: for instance they are of finite global dimension and BGG-reciprocity holds. In general, determining whether a length abelian category with finitely many simple objects is highest weight (the case which I will consider in this talk) is a hard problem. I will recall a result that relates highest weights categories and the existence of some special recollements. Then, I will introduce stability conditions and show how the existence of stability conditions which satisfy some additional properties can be used to detect highest weight categories.

This is ongoing joint work with Jon Woolf.