The University of Michigan Combinatorics Seminar


Abstract 

The simplest cluster algebras are those associated to triangulations of a polygon. I will be mainly interested, not in the usual cluster algebras, but in their tropical version, as in work of GekhtmanShapiroVainshtein and FominThurston. I will discuss a higherdimensional generalization of this framework, in which the polygon has been replaced by an evendimensional cyclic polytope. In this setting, we find an analogue of the tropical cluster algebra. I will discuss various aspects of the usual theory which generalize, and some which don't. I will touch only briefly on the higherdimensional analogue of the link from cluster algebras to tilting theory of hereditary algebras and the cluster category, since that will be the topic of my talk on Tuesday, September 21, in the Algebra seminar. (The two talks will be independent, and I will try to keep overlap to a minimum.)
