Alejandro Vargas: Tropical morphisms to metric trees

Following the prevailing philosophy in Tropical Geometry of posing and solving analogues of classical problems in the tropical world, we will present the combinatorial aspects of the tropical analogue to the problem of calculating curve gonality. Metric graphs and metric trees are the analogues to algebraic curves and the projective line. We use a deformation argument to construct for every metric graph a map satisfying certain conditions to a tree. When g := |E(G)| - |V(G)| + 1 is even, we do a count of such maps and get the g/2-th Catalan number.