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Explore the intricacies of box-ball systems in this comprehensive lecture by Masato Okado. Delve into the reasons why box-ball systems are considered integrable from the perspective of quantum integrable systems, with a focus on the crucial role of the combinatorial Yang-Baxter equation. Examine the extent to which this situation can be generalized, covering known results such as Kirillov-Reshetikhin crystals and path to rigged configuration bijection. Gain insights into recent work on new solutions of the combinatorial reflection equation, which allows for the formulation of box-ball systems with boundary. This in-depth presentation, part of the Workshop on box-ball systems from integrable systems and probabilistic perspectives, offers a thorough review and exploration of recent developments in the field.
