The box-ball system and cyclindric loop Schur functions
The box-ball system is a cellular automaton in which a sequence of balls moves along a row of boxes. An interesting feature of this automaton is its soliton behavior: regardless of the initial state, the balls in the system eventually form themselves into connected blocks (solitons) which remain together for the rest of time.
In 2014, T. Lam, P. Pylyavskyy, and R. Sakamoto conjectured a formula which describes the solitons resulting from an initial state of the box-ball system in terms of the tropicalization of certain polynomials they called cylindric loop Schur functions. In this talk, I will describe the various ingredients of this conjecture and discuss its proof.