| 研究者所属（当時） | 資格 | 氏名 | |
|---|---|---|---|
| （代表者） | 高等研究所 | 講師 | ストークス アレクサンダー ヘンリー |
| （連携研究者） | BIMSA | Associate Professor | Anton Dzhamay |
| （連携研究者） | The University of Tokyo | Assistant Professor | Takafumi Mase |
| （連携研究者） | The University of Tokyo | Professor | Ralph Willox |
| （連携研究者） | The University of Sydney | Research Associate | Pieter Roffelsen |
| （連携研究者） | Flinders University | Senior Lecturer | Yang Shi |
| （連携研究者） | Université Paris-Saclay and Université de Paris-Cité | Professor | Basile Grammaticos |
| （連携研究者） | University of Warsaw | Associate Professor | Galina Filipuk |
| （連携研究者） | SISSA | Postdoc | Michele Graffeo |
| （連携研究者） | University of Milan | Associate Professor | Giorgio Gubbiotti |
- 研究成果概要
Painlevé equations, both differential and discrete, are nonlinear models in two dimensions with wide applications in mathematics and physics. Despite being nonlinear they are integrable (which, roughly speaking, means they exhibit ordered behaviour rather than chaos), and many of their properties can be understood through their association to a special class of geometric objects called generalised Halphen surfaces. This research fits within a broader program of extending this geometric framework, as well as the suite of tools it provides for the analysis of Painlevé equations, to both discrete Painlevé equations in higher dimensions and to delay-differential Painlevé equations, which are infinite-dimensional systems.
The research conducted during the period funded by the grant has made significant progress on the geometry of higher-dimensional analogues of discrete Painlevé equations, geometric approaches to differential Painlevé equations appearing as higher-dimensional systems subject to some constraint, and related problems in the study of integrability and geometry more broadly. In particular, it has led to the establishment of the geometric structure of examples of multiplicative-type higher-dimensional discrete Painlevé equations for the first time. It has also led to insights into the algebraic structure of symmetries of discrete Painlevé equations, which will be used in further developing a geometric theory in higher dimensions.
Some concrete research outputs of the project are listed below, including 2 published papers, 1 paper under review for publication, and 6 presentations at domestic and international conferences. The results obtained during the grant period have set a strong foundation for the continued pursuit of the research over the next years, and several more papers are in preparation.