Daniel Labardini

To each triangulation of a surface with marked points it is possible associate a quiver (=digraph) and a potential (=linear combination of oriented cycles) in a quite natural way. A few years ago I proved that the effect of a flip of a triangulation on the associated quiver with potential is that of "mutation", an operation arising in cluster algebras. In this talk I will present some of the combinatorial ingredients in the proof of this result, as well as a brief overview of the applications it has had in recent years.