By Gérard Duchamp
By Cyril Banderier
By Karol Penson
By Bea Schumann
Appears in collection : Combinatorics and Arithmetic for Physics: special days
We study defining inequalities of string cones via a potential function on a reduced double Bruhat cell. We give a necessary criterion for the potential function to provide a minimal set of inequalities via tropicalization and conjecture an equivalence. This is based on joint work with Gleb Koshevoy.