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

tt* 方程：模空间微分几何与经典等单性理论之间的桥梁

• 批准号: 18H03668
• 负责人: Guest Martin
• 金额: $ 18.55万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (A)
• 财政年份: 2018
• 资助国家: 日本
• 起止时间: 2018-04-01 至 2023-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-18H03668/
• 关键词: Integrable systems; Geometry; Quantum cohomology; tt* equations; Isomonodromy; tt＊ equations

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.

主要研究者与A. IUPUI，USA）和C.- S. Lin（NTU，Taiwan）在SL（n，R）情形下描述了tt*-户田方程的所有整体解，其中n为任意值. 关于这一主题的全面文章正在编写中。首席研究员和共同研究员Otofuji也在Virasoro代数表示在tt* 方程理论中的作用方面取得了进展。这导致了关于这一主题的计划系列出版物的第一部。共同研究员细野继续他的研究K3流形，并获得了进一步的新结果。主要研究者和合作研究者细野发起了与A.金泽从调和映射理论的角度讨论了tt* 方程在K3流形理论中的作用。举行了“特殊几何与可积系统”在线会议（从2020年延期），外国演讲者包括V.科尔特斯（汉堡）、C. Hertling（曼海姆），Ian斯特拉坎（格拉斯哥），A. Swann（Aarhus）以及共同研究员Hosono和Iritani。 客座兼联合研究员Ohnita共同组织了第三届日本-台湾微分几何在线联席会议。 举办了一次关于“户田方程、抛物线希格斯束和相关专题”的在线讲习班。第13届MSJ-SI“微分几何和可积系统”（从2020年推迟）的第一部分在年底以混合格式举行。

项目成果

Hamiltonian aspects of the tt*-Toda equations

tt*-Toda 方程的哈密顿量方面

• 发表时间: 2019
• 作者: 石田洋子;吉田和浩;萱島信子;黒田一雄ほか;Martin Guest
• 通讯作者: Martin Guest

Differential Geometry and Integrable Systems

微分几何和可积系统

• 发表时间: 2022

K3 surfaces from configurations of six lines in P2 and mirror symmetry II-- λK3 -functions

K3 表面来自 P2 中的六条线的配置和镜像对称 II-- λK3 - 函数

• DOI: 10.1093/imrn/rnz259
• 发表时间: 2019
• 期刊: International Mathematics Research Notices
• 影响因子: 1
• 作者: S. Hosono;B.H. Lian and S.-T. Yau
• 通讯作者: B.H. Lian and S.-T. Yau

Quantum cohomology: is it still relevant?

量子上同调：它仍然相关吗？

• 发表时间: 2021
• 作者: K. Shimakawa;K. Yoshida and T. Haraguchi;Yuichi YAMADA;山田裕一;山田裕一;Martin Guest
• 通讯作者: Martin Guest

The (enhanced) Coxeter Plane: an application of differential equations to Lie theory

（增强的）Coxeter 平面：微分方程在李理论中的应用

• 发表时间: 2019
• 作者: Martin Guest