Application of Abelian function theory to Integrable system
| Project/Area Number |
16K05187
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Sasebo National College of Technology |
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Principal Investigator |
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| Research Collaborator |
Komeda Jiryo
Previato Emma
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 代数曲線 / アーベル関数 / σ関数 / 可積分系 / 産業数理 / アーベル関数論 / 退化族 / ヤコビ多様体 / 戸田格子 / ワィエルシュトラス正規形式 / 数値半群 / 退化 / 可積分 / 弾性曲線 |
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| Outline of Final Research Achievements |
We have the following results: 1) The determination of the Riemann constant for every algebraic curve which is given by the Weierstrass normal form even with non-symmetric numerical semigroup as Weierstrass non-gap at its infinity, 2) Jacobi inversion formulae for a general Weierstrass normal form, 3) Clarification of the relation between covering of the curve and correspondence of the hyperelliptic quasi-periodic solution to periodic solution of the Toda lattice equation, 4) Formulation of the behavior of sigma function for a degeneration of trigonal cyclic curve, 5) Relation of the MKdV hierarchy of the isometric deformation of curve in a plane and the Faber polynomial, and 6) Applications of mathematics to other fields (Quantum walk and coloring, Graph zeta function and conductivity of carbon, path space of the Lie group and robotics, algebraic description of screw dislocation)
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| Academic Significance and Societal Importance of the Research Achievements |
本研究は、数学以外の分野への応用を見据えて、アーベル関数を楕円関数と同レベルの具体性を持つように再構築し、その再構築の結果と可積分系を通して他分野へアーベル関数論を適用することを目指すものである。また、適用に向け、幅広い数学の異分野への応用も含め、数学が社会に役立つ事を示すことは重要である。上記成果は、このような方向性に沿った結果である。
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Report
(4 results)
Research Products
(30 results)
