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2017 Fiscal Year Final Research Report

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

Research Project

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Project/Area Number 25247005
Research Category

Grant-in-Aid for Scientific Research (A)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionWaseda 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
KeywordsIntegrable 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

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Published: 2019-03-29  

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