表題番号：2023E-021
日付：2024/04/04
研究課題tt*-戸田方程式のシンプレクティック幾何学
| 研究者所属（当時） | 資格 | 氏名 | |
|---|---|---|---|
| （代表者） | 理工学術院 基幹理工学部 | 助手 | 大土井 亮祐 |
| （連携研究者） | Waseda University | Professor | Martin Guest |
| （連携研究者） | Indiana University-Purdue University Indianapolis | Professor | Alexander Its |
| （連携研究者） | Gettysburg College | Visiting Assistant Professor | Maksim Kosmakov |
| （連携研究者） | Indiana University-Purdue University Indianapolis | Ph. D. Student | Kenta Miyahara |
- 研究成果概要
- To solve the Riemann-Hilbert problem related to the tt*-Toda equation, we solved a Riemann-Hilbert problem related to the radial two-dimensional Toda lattice, which is obtained by changing the signs of the coefficients of the tt*-Toda equations. As a result, we obtained connection formulae. While the connection formulae themself are not new, previous studies obtained them using WKB analysis. In contrast, our approach utilized the Deift-Zhou nonlinear steepest descent method, extending the existing research from the case of 2×2 matrices to 3×3 matrices, which is a novel contribution. Research on the general case of n×n matrices is also ongoing. We summarized the results into a paper, as indicated in the achievements section, and it is currently under submission. Additionally, presentations were given, as noted in the achievements section (one in August 2023, which was about research results before then, and two in March 2024, which were related to the above).