Viewpoints Brought by the Box and Ball System

Explore the fascinating world of box and ball systems in this 52-minute lecture by Daisuke Takahashi at the Centre de recherches mathématiques (CRM). Delve into the concept of an ultimately discretized integrable system that realizes solitons in a digital environment. Discover how this system, initially found as a cellular automaton for advection, emerges through ultradiscretization (also known as tropicalization or crystallization) of difference soliton equations. Learn about the max-plus system that results from this process and how it embeds cellular automata. Gain insights into the system's discovery and subsequent developments, including its applications in traffic flow modeling, pattern formation, chaos theory, and Lyapunov functions. Explore the connections between box and ball systems and lattice equations, with a particular focus on ultradiscretization and max-plus/max-min representations. This lecture, part of a workshop on box-ball systems from integrable systems and probabilistic perspectives, offers a comprehensive overview of this intriguing mathematical concept and its wide-ranging implications.