Systematic development and application of methods in differential geometry and integrable systems motivated by quantum cohomology

2017 Fiscal Year Final Research Report

• Project/Area Number: 25247005
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Waseda University
• Principal Investigator: Guest Martin 早稲田大学, 理工学術院, 教授 (10295470)
• Co-Investigator(Renkei-kenkyūsha): OHNITA Yoshihiro 大阪市立大学, 理学研究科, 教授 (90183764) ; MAEDA Yoshiaki 東北大学, 知の創出センター, 副センター長 (40101076) ; SERGEI V Ketov 首都大学東京, 理工学研究科, 准教授 (70347269) ; SAKAI Takashi 首都大学東京, 理工学研究科, 准教授 (30381445) ; OTOFUJI Takashi 日本大学, 工学部, 准教授 (70339266) ; AKAHO Manabu 首都大学東京, 理工学研究科, 准教授 (30332935) ; KOBAYASHI Shimpei 北海道大学, 理学研究科, 准教授 (40408654) ; IRITANI Hiroshi 京都大学, 理学研究科, 教授 (20448400) ; HOSONO Shinobu 学習院大学, 理学部, 教授 (60212198)
• Project Period (FY): 2013-10-21 – 2018-03-31
• Keywords: Integrable systems / Geometry / Quantum cohomology

Outline of Final Research Achievements

A series of methods for solving the tt*-Toda equations were developed during the course of this project. These methods used p.d.e. theory, integrable systems theory, and Lie theory. Our main results were achieved for the tt*-Toda equations of type A_n. Here we give a complete treatment of the solutions and their asymptotic data and monodromy data. A more abstract approach was used in the case n=1, in order to describe the moduli space of solutions. These results were motivated in part by the special solutions corresponding to quantum cohomology rings of Kaehler manifolds. In order to promote research in this area, a number of conferences, workshops, and seminars by specialists were organised.

Free Research Field

数物系科学, 微分幾何学