Georgia Institute of Technology College of Sciences

Every graph G has canonically associated to a finite abelian group called the Jacobian group. The cardinality of this group is the number of spanning trees in G. If G is planar, the Jacobian group admits a natural simply transitive action on the set of spanning trees. More generally, for any graph G one can define a whole family of (non-canonical) simply transitive group actions. The analysis of such group actions involves ideas from tropical geometry. Part of this talk is based on joint work with Yao Wang, and part is based on joint work with Spencer Backman and Chi Ho Yuen.