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.

首席研究人员与A.（美国IUPUI）和C.-S.合作取得了进展。 lin（NTU，台湾）在SL（n，r）的情况下描述了TT*-TODA方程的所有全局解决方案，用于任意n。 有关此主题的全面文章正在准备。首席研究者和共同研究者Otofuji也对Virasoro代数表示在TT*方程理论中的作用也取得了进展。这导致了有关该主题的计划的第一次出版物。共同投资者Hosono继续对K3歧管的研究，并获得了进一步的新结果。首席研究员和共同入选者Hosono与A. Kanazawa启动了TT*方程在K3理论中的作用，从Harmonic Map理论的角度来看，K3歧管理论。 （格拉斯哥），A。Swann（Aarhus），以及共同投资者Hosono和Iritani。 来宾和共同投资者Ohnita共同组织了在线第三台台湾差异几何联合会议。 在“ Toda方程，抛物线式希格斯捆绑包和相关主题”上举行了一个在线研讨会。第13个MSJ-SI“差异几何和可集成系统”（从2020年推迟）的第一部分以混合形式在年底以混合形式举行。

项目成果

Differential Geometry and Integrable Systems

微分几何和可积系统

• 发表时间: 2022

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

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

K3 surfaces from configurations of six lines in P2 and mirror symmetry I

K3 表面来自 P2 中的六条线的配置和镜像对称 I

• DOI: 10.4310/cntp.2020.v14.n4.a2
• 发表时间: 2020
• 期刊: Communications in Number Theory and Physics
• 影响因子: 1.9
• 作者: Shinobu Hosono and Hiromichi Takagi;Shinobu Hosono and Hiromichi Takagi
• 通讯作者: Shinobu Hosono and Hiromichi Takagi

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