| Lecture | Time | Place |
|---|---|---|
| Lecture 1 | 09:00-10:30, 14.04.2025 | Main Lecture Hall, Ex-Isef |
| Lecture 2 | 14:15-15:45, 15.04.2025 | Main Lecture Hall, Ex-Isef |
| Lecture 3 | 10:45-12:15, 16.04.2025 | Main Lecture Hall, Ex-Isef |
| Lecture 4 | 09:00-10:30, 17.04.2025 | Main Lecture Hall, Ex-Isef |
Date: 14 April 2025 - 17 April 2025
Abstract:
In recent years, there has been growing interest in the study of integrable systems from the perspectives of statistical mechanics and probability theory. The theory of generalized hydrodynamics, developed by mathematical physicists, suggests that the macroscopic behavior of integrable systems is highly universal. To mathematically substantiate such theories with concrete models, a type of cellular automaton called the box-ball system (BBS) has been extensively studied by probabilists in recent years. The BBS, which exhibits solitonic behavior, has been studied from various viewpoints, such as tropical geometry, combinatorics, and representation theory, over 30 years. However, research from the probabilistic perspective began only about 10 years ago. Recently, probabilistic approaches, including the application of the Pitman transform, analysis of invariant measures, and scaling limits, have rapidly expanded. These have revealed new connections between probability theory and classical integrable systems, showing that the macroscopic behavior of integrable systems exhibits a universality distinct from that of chaotic systems.
In this lecture, I will introduce these new research topics, mainly focusing on the box-ball system, and present the rigorous results obtained in the past several years, starting from the basic concepts.