The tt* equations: a bridge between the differential geometry of moduli spaces and classical isomonodromy theory

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Progress was made by Principal Investigator in collaboration with A. Its (IUPUI, USA) and C.-S. Lin (NTU, Taiwan) on describing all global solutions of the tt*-Toda equations in the case of SL(n,R), for arbitrary n. A comprehensive article on this topic is in preparation. Progress was also made by Principal Investigator and Co-Investigator Otofuji on the role of representations of the Virasoro algebra in the theory of the tt* equations. This resulted in the first of planned series of publications on this topic. Co-Investigator Hosono continued his research on K3 manifolds and obtained further new results. The Principal Investigator and Co-Investigator Hosono initiated a collaboration with A. Kanazawa on the role of the tt* equations in the theory of K3 manifolds from the point of view of harmonic map theory.An online conference on "Special Geometry and Integrable Systems" (postponed from 2020) was held with foreign speakers including V. Cortes (Hamburg), C. Hertling (Mannheim), Ian Strachan (Glasgow), A. Swann (Aarhus), as well as Co-Investigators Hosono and Iritani. Guest and Co-Investigator Ohnita co-organised the online 3rd Japan-Taiwan Joint Conference on Differential Geometry. An online workshop was held on "Toda equations, parabolic Higgs bundles, and related topics". The first part of the 13th MSJ-SI "Differential Geometry and Integrable Systems" (postponed from 2020) was held in hybrid format at the end of the year.