Search for new connection of integrable systems and mathematical physics

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"Integrable systems" is a collective name for "solvable" mathematical models. They are mostly a differential equation, but some cases are formulated as a probability distribution or a stochastic process. Integrable systems are interesting not only because they can be solved by a systematic method, but also remarkable for rich mathematical structures hidden behind. In this research project, we sought for new material in mathematical physics after 2000, and obtained several results on integrable systems themselves and on their applications to gauge theory and string theory. These results are expected to lead to new research.