| Project/Area Number |
18K03281
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Review Section |
Basic Section 11020:Geometry-related
|
|---|
| Research Institution | Bunkyo University (2020-2023)
Kagawa University (2018-2019) |
|---|
Principal Investigator |
Satake Ikuo 文教大学, 教育学部, 教授 (80243161)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
藤 博之 大阪工業大学, 情報科学部, 教授 (50391719)
|
|---|
| Project Period (FY) |
2018-04-01 – 2024-03-31
|
| Project Status |
Completed (Fiscal Year 2023)
|
| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2019: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
|---|
| Keywords | フロベニウス多様体 / 位相的漸化式 / Frobenius 多様体 / コクセター変換 / 振動積分 / 行列模型 / Frobenius多様体 / 原始形式 |
|---|
| Outline of Final Research Achievements |
Principal investigator Satake approached the case where the LG model is defined by a one-variable potential with a concrete example. However the case of one-variable was solved by Milanov's discussion of primitive forms and topological recursion for Hurwitz coverings, which gave a high-species oscillatory integral representation.
In order to use the coverings obtained from periodic maps as spectral curves of the LG model defined by multivariate potentials, the theory of Good invariants was developed. This also gave a new perspective on finite mirror group invariants.
Fuji, a co-researcher of this project, studied topological recursion and clarified the physical meaning of geometric quantities such as the Masur-Veech volume, which has been studied in hyperbolic geometry.
|
| Academic Significance and Societal Importance of the Research Achievements |
位相的漸化式のアイデアは、特異点理論、振動積分、フロベニウス多様体、Gromov-Witten 不変量などミラー対称性として知られていた対応のみならず、双曲幾何学におけるMasur-Veech体積、結び目の不変量なども横断的に視野に入れることを要求しており、各分野での深いアイデアを交流させることができる。コクセター変換という、鏡映群不変式においてもその特異な位置を占める変換が、この研究成果により Frobenius 多様体の構造そのものを導くことがわかったため、今後は普遍的な内容として他分野での新たな位置づけを得ていくことは、学術的に意義があると考えている。
|
