2012 Fiscal Year Final Research Report
Exploitation of new relations between differential geometry and quantum cohomology in the context of integrable systems
| Project/Area Number |
21244004
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Waseda University (2012)
Tokyo Metropolitan University (2009-2011) |
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Principal Investigator |
GUEST Martin 早稲田大学, 理工学術院, 教授 (10295470)
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| Co-Investigator(Renkei-kenkyūsha) |
KAMISHIMA Yoshinobu 首都大学東京, 理工学研究科, 教授 (10125304)
TOKUNAGA Hiroo 首都大学東京, 理工学研究科, 教授 (30211395)
MAEDA Yoshiaki 慶應大学, 理工学部, 教授 (40101076)
MIYAOKA Reiko 東北大学, 理学研究科, 教授 (70108182)
KOHNO Toshitake 東京大学, 数理科学研究科, 教授 (80144111)
OHNITA Yoshihiro 大阪市立大学, 大学院・理学研究科, 教授 (90183764)
SAKAI Takashi 首都大学東京, 理工学研究科, 准教授 (30381445)
SERGEI V Ketov 首都大学東京, 理工学研究科, 准教授 (70347269)
AKAHO Manabu 首都大学東京, 理工学研究科, 助教 (30332935)
OTOFUJI Takashi 日本大学, 工学部, 講師 (70339266)
KOBAYASHI Shinpei 弘前大学, 大学院・理工学研究科, 助教 (40408654)
KUROSU Sanae 東京理科大学, 理学部, 助教 (70457844)
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| Project Period (FY) |
2009 – 2012
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| Keywords | 幾何学 / 可積分系 / 量子コホモロジー |
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| Research Abstract |
We have made progress with some key examples, which demonstrate interesting and nontrivial phenomena. In "Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa" (M. Guest and C.-S. Lin, J. reine angew. Math., 2012, in press) the existence of a family of smooth solutions of the tt*-Toda equation was established. This was a technical breakthrough: p.d.e. methods are well suited to the noncompact case, where standard loop group methods fail. In "Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data" (M. Guest, A. Its, and C.-S. Lin, arXiv:1209.2045), a second technical breakthrough was made, by relating the global smoothness of the solutions to the monodromy data (Stokes data) of an associated linear equation. This Stokes data was computed explicitly for all globally smooth solutions of the tt*-Toda equation. We expect that these techniques will be applicable to other problems in differential geometry.
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Research Products
(53 results)
