KP2 solitons: a comparison between the combinatorial and the geometrical approach in the direct and inverse spectral problem

In this talk we shall review recent papers by Abenda-Grinevich, Ichikawa, Nakayashiki, Agostini-Fevola-Mandelshtam-Sturmfels, Fevola-Mandelshtam and Kodama, and explain the role of tropical geometry and combinatorics in the solution to the direct and inverse spectral problems for KP2 solitons.