The operation of mutation has a long history in representation theory and algebraic geometry, be it in the context of exceptional collections of sheaves or in the combinatorial study of tilting modules. The aim is to create a new object from an old one by changing a designated part of it and keeping the other part. Here I discuss a variant in the context of cosilting objects in compactly generating triangulated categories (which are also known as derived injective cogenerators for t-structures of Grothendieck type). In that case, the operation of mutation corresponds to certain nice tilts of t-structures with respect to torsion pairs. Time permitting, I will explain how this is related to the lattice of torsion pairs in the category of finite-dimensional modules over a finite-dimensional algebra, as studied by Demonet, Iyama, Reading, Reiten and Thomas.
This is joint work with Lidia Angeleri Hügel, Rosanna Laking and Jorge Vitória.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
