This series of talks is based on joint works with Oppermann, Grimeland, Labardini and Plamondon. Cluster categories are triangulated categories where quiver mutation appears as a natural operation. A first class of example is given by cluster categories associated with surfaces with marked points. A second class is constructed using the derived category of finite-dimensional algebras of global dimension 2. Mixing both constructions, one may consider surface cut algebras, that are algebras of global dimension 2 constructed from a surface and show how cluster combinatorics permits to deduce information on their derived category.
These videos were produced by Syracuse University Department of Mathematics as part of ICRA 2016.
