2017 Fiscal Year Annual Research Report
Systematic development and application of methods in differential geometry and integrable systems motivated by quantum cohomology
| Project/Area Number |
25247005
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| Research Institution | Waseda University |
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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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| Project Period (FY) |
2013-10-21 – 2018-03-31
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| Keywords | Integrable systems / Geometry / Quantum cohomology |
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| Outline of Annual Research Achievements |
The tt*-Toda equations (certain differential equations which play an important role in supersymmetry, differential geom etry, and integrable systems) were the main focus of our research. Motivated by quantum cohomology, we developed and ap plied methods to solve these equations.
The third article in the series "Isomonodromy aspects of the tt* equations of Cecotti and Vafa I,II,III" written jointly with A. Its (IUPUI, USA) and C.-S. Lin (National Taiwan University)was finished, thus giving a complete picture of the solutions of the tt*-Toda equations and their asymptotics in the case of two independent functions. The article "Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations" written jointly with N.-K. Ho (National Tsinghua University, Taiwan) was finished, thus giving a Lie-theoretic foundation for some of the results in the joint work with Its and Lin. Final modifications were made to the article "Painleve III: A Case Study in the Geometry of Meromorphic Connections" written jointly with C. Hertling (Mannheim, Germany).
Several workshops and conferences related to this project were organised. The main activity was the conference "Differential Geometry and Differential Equations: the influence of Mirror Symmetry and Physics", which was held 11-15 December 2017 at Waseda University. A study meeting on the theme "Noncommutative geometry and related topics" was held in the framework of the Koriyama Geometry and Physics Days at Nihon University (Koriyama, Fukushima), 23-24 February 2018.
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| Research Progress Status |
29年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
29年度が最終年度であるため、記入しない。
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