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

首席调查员与A.ITS(IUPUI，美国)和C.S.Lin(台大，台湾)合作，在描述任意n的SL(n，R)情况下TT*-Toda方程的所有整体解方面取得了进展。关于这一专题的一篇综合文章正在编写中。首席研究员和联合研究员Otofuji在关于Virasoro代数的表示在TT*方程理论中的作用方面也取得了进展。这导致了计划中关于这一主题的系列出版物的第一次出版。合作研究员细野继续他对K3流形的研究，并获得了进一步的新结果。首席研究员兼合作研究员Hosono从调和映射理论的角度与A.Kanazawa合作，讨论TT*方程在K3流形理论中的作用。在线会议(从2020年推迟)举行，外国演讲者包括V.Cortes(汉堡)、C.Herting(Mannheim)、Ian Strachan(Glasgow)、A.Swann(Aarhus)以及共同研究员Hosono和Iritani。嘉宾和合作研究员Ohnita共同组织了第三届日本-台湾微分几何在线联合会议。举办了一个关于“Toda方程、抛物线Higgs丛和相关主题”的在线研讨会。第十三届MSJ-SI《微分几何与可积系统》(从2020年推迟)的第一部分于年底以混合形式举行。

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.