Box-ball systems are a discrete dynamical system analog of the Kortewig–de Vries equation described by the simple process of moving balls in boxes. The soliton solutions of such systems correspond to packets of balls moving together. An interpretation using Kashiwara’s theory of crystals allows the box-ball systems to be generalised using combinatoric methods. Utilising ideas from supersymmetry, a different generalisation was introduced by Hikami and Inoue. Recently, a corresponding analog of the crystal theory was given by Kwon and Okado, giving a method to generalise the Hikami-Inoue system.
This project will use the results of Kwon and Okado to describe a new discrete dynamical system that generalises the supersymmetric box-ball system of Hikami and Inoue, by using the combinatorial R-matrix from Kwon and Okado to describe the time evolution. The goal of the project is to generalise the description of solitons in SCA (soliton cellular automata) to define a soliton in our new system.
The University of Queensland
Benjamin Solomon is an undergraduate student of The University of Queensland studying Bachelors of Mathematics and Science. His mathematical interest presides in the area of Abstract Algebra, in particular, representation theory and its application in quantum mechanics. During his second year of study Benjamin began reading research papers to explore fields that he was interested in. During this process, he began meeting with post graduates to discuss their research. This lead to participating in research in the area of representation theory and combinatorics during the year 2020.