Georgia Institute of Technology College of Sciences

In classical algebraic geometry,Torelli's theorem states that a complete smooth curve over an algebraically closed field is uniquely determined by its principally polarized Jacobian. We will investigate a tropical analogue of this theorem. Torelli's problem for tropical curves is intimately related to some basic combinatorial questions regarding the cycle space of a finite graph. Combinatorics of the Voronoi (or Delaunay) decomposition associated to the cycle lattice play an essential role. This talk will be self-contained. The talk next week (by Melody Chan) can be considered a natural sequel.