Séminaire de Géométrie Tropicale
Mercredi 14 octobre 2015 14h salle 1525-502
Rei Inoue
(Chiba University)
Tropical geometry and combinatorics in integrable cellular automata
Résumé :
The box-ball system (BBS) is an integrable cellular automaton invented in 1990,
which is given by a simple rule to move finite number of balls
in boxes arranged in a line (or in a circle).
In this talk I will introduce the BBS and its integrable structure
clarified in this century.
The initial value problem of the BBS is solved
by using a combinatorial map called Kerov-Kirillov-Reshetikhin bijection.
Via the map, the nonlinear time evolution of the BBS is mapped to
a linear motion on a high-dimensional torus.
Interestingly, this torus turns out to be the tropical Jacobian variety
of a hyperelliptic tropical curve.