| Outline of Annual Research Achievements |
Progress this year was mainly related to sub-project (a) on the tt*-Toda equations. The preprint "The tt*-Toda equations of A_n type" (M. A. Guest, A. R. Its, and C.-S. Lin , arXiv:2302.04597) was completed. A new project was initiated, jointly with Tadashi Udagawa (Waseda University), on a construction by Cecotti-Vafa of solutions of the tt* equations from the SU(2)_k fusion ring. Discussions were held with Katrin Wendland (Trinity College Dublin) on the classification of conformal theories using modular differential equations. Discussions were held with River Chiang, Nan-Kuo-Ho, and Eckhard Meinrenken on the symplectic structure of the space of solutions of the tt*-Toda equations.
Several research activities were partially supported. Guest was a co-organiser of the international conference "Geometry, Stochastics & Dynamics: Celebrating 20 years of UK-Japan Winter Schools" in September 2022 (postponed from 2020) at Imperial College London. A workshop on symplectic geometry and its applications was held in October 2022 at Waseda University. Guest and Ohnita co-organised the second part of the 13th MSJ-SI "Differential Geometry and Integrable Systems" in November 2022 at Takamatsu. Guest organised a course on "Modular Forms in Geometry and Physics" in December 2022, and an associated workshop in January 2023, at Waseda University.
Other visiting specialists from abroad included River Chiang (NCKU, Taiwan), Nan-Kuo-Ho (NTHU, Taiwan), Omar Kidwai (Birmingham, UK), Ian McIntosh (York, UK), Eckhard Meinrenken (Toronto, Canada), Claudio Meneses (Kiel, Germany).
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