| 研究課題/領域番号 |
21K03292
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| 研究機関 | 名古屋大学 |
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研究代表者 |
Richard Serge 名古屋大学, 教養教育院, 教授 (70725241)
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| 研究期間 (年度) |
2021-04-01 – 2025-03-31
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| キーワード | Singular integrals / Special functions / scattering theory / surface states / Index theorems |
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| 研究実績の概要 |
The research activities can be summarized as follows:
1) The investigations with H. Inoue on scattering theory and an index theorem on the radial part of SL(2,R) have been completed and a manuscript submitted. It is the first application of Levinson's theorem in group representations, and involves numerous special functions.
2) The two works with T. Miyoshi and Q. Sun have been completed, submitted for publication, and one has been published, the other one accepted. These works involve data assimilation techniques and have been developed because of the restrictions due to the COVID-19 pandemic.
3) The investigations on surface states have been the main topic for this FY and the work is nearly completed. D. Parra and A. Rennie have joined the team for this project. A manuscript will probably be submitted in Spring 2023.
4) A new research project has started with A. Rennie about 2D Schroedinger operators with exceptional singularities at 0 energy. The initial problem involves a very singular integral kernel, and it is expected that the solution will involve a product of special functions.
5) A new project on Mourre theory and some propagation estimates has started during the stay of N. Boussaid in Nagoya in Fall 2022. Preliminary results are promising, but further investigations are necessary.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
1: 当初の計画以上に進展している
理由
With the end of the pandemic and the opening of the borders, it has been possible to resume the activities, invite colleagues from abroad, and organize business trips. All researchers enjoy having again in person interactions. This enthusiasm is visible on research activities and on the research progress.
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| 今後の研究の推進方策 |
The research activities 3), 4), and 5) will continue. Invitations or business trips will be organized according to these projects. In addition, there are discussions about the project of writing a book with my best collaborator R. Tiedra de Aldecoa. This project would be the culmination of 20 years of collaboration, and is a huge but very appealing project. Preliminary investigations are currently performed.
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| 次年度使用額が生じた理由 |
The amount is very small and will be used appropriately in the new fiscal year.
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