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

2023 Fiscal Year Final Research Report

• Project/Area Number: 18H03668
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Medium-sized Section 11:Algebra, geometry, and related fields
• Research Institution: Waseda University
• Principal Investigator: GUEST Martin 早稲田大学, 理工学術院, 教授 (10295470)
• Co-Investigator(Kenkyū-buntansha): 細野 忍 学習院大学, 理学部, 教授 (60212198) ; 大仁田 義裕 大阪公立大学, 数学研究所, 特別研究員 (90183764)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: Integrable systems / Quantum cohomology / tt* equations / Isomonodromy

Outline of Final Research Achievements

The research activities of this project led to several new mathematical results on the tt*-Toda equations, and to a deeper understanding of theoretical aspects of supersymmetry. All solutions on C* of the tt*-Toda equations for the Lie group G = SL(n,C) were found, and all their asymptotic data and monodromy data were computed. For any complex simple Lie group G, the asymptotic data of solutions at infinity, and their relation to Stokes data, was elucidated in Lie-theoretic terms. A physical interpretation of this data was found. Activities such as lecture series, seminars, workshops, and conferences were carried out jointly with Co-Investigators. These activities facilitated the interaction of researchers in both classical and modern methods.

Free Research Field

数物系科学, 微分幾何学

Academic Significance and Societal Importance of the Research Achievements

The research results obtained during this project were published in international scientific journals. They were also made publicly available at https://arxiv.org/. They contributed to an active area of mathematical research related to physics, and to the training of young researchers.