Georgia Institute of Technology College of Sciences

I will continue the discussion on the group actions of the graph Jacobian on the set of spanning trees. After reviewing the basic definitions, I will explain how polyhedral geometry leads to a new family of such actions. These actions can be described combinatorially, but proving that they are simply transitive uses geometry in an essential way. If time permits, I will also explain the following surprising connection: the canonical group action for a plane graph (via rotor-routing or Bernardi process) is related to the canonical tropical geometric structure of its dual graph. This is joint work with Spencer Backman and Matt Baker.