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.

首席研究员与 A.Its（IUPUI，美国）和 C.-S 合作取得了进展。 Lin（NTU，台湾）描述了 SL(n,R) 情况下 tt*-Toda 方程的所有全局解，对于任意 n。 关于该主题的综合文章正在准备中。首席研究员和联合研究员 Otofuji 在 Virasoro 代数表示在 tt* 方程理论中的作用方面也取得了进展。这导致了有关该主题的计划系列出版物中的第一篇。共同研究员细野继续对K3流形进行研究，并获得了进一步的新结果。首席研究员兼副研究员Hosono发起与A. Kanazawa的合作，从调和映射理论的角度探讨tt*方程在K3流形理论中的作用。“特殊几何与可积系统”在线会议（从 2020 年推迟）与外国演讲者一起举行，包括 V. Cortes（汉堡）、C. Herdling（曼海姆）、Ian Strachan（格拉斯哥）、 A. Swann（奥尔胡斯），以及联合调查员 Hosono 和 Iritani。 嘉宾和共同研究员 Ohnita 共同组织了在线第三届日本-台湾微分几何联合会议。 举办了关于“Toda 方程、抛物线希格斯丛及相关主题”的在线研讨会。第13届MSJ-SI“微分几何与可积系统”（2020年推迟）第一部分于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

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