| 研究課題/領域番号 |
26707005
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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, 多元数理科学研究科, 特任准教授 (70725241)
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| 研究期間 (年度) |
2014-04-01 – 2017-03-31
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| キーワード | spectral theory / scattering theory / wave operators / index theorem / periodic systems |
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| 研究実績の概要 |
During this second year we consolidated the progresses already made and developed some new collaborations. The stay of R. Tiedra in March - April 2015 led to a short publication which has been submitted in the fall. The report from the journal has not been received yet. From mi-March to mid-August, my PhD student from France visited me in Nagoya. His initial work is almost completed, and during his stay we completed and submitted a paper on the continuity of the spectra for families of discrete magnetic operators. The paper will appear in the journal "Analysis and mathematical physics".
As initially planed, our collaborator J. Kellendonk visited us for one week, and we both attended a conference on topological insulators in Sendai in October. Our horizon has been broaden by this new subject of research which also lies at the interface between analysis and non-commutative geometry.
The second part of the year has been devoted to the project with J. Derezinski (from Warsaw) and a 61 pages paper has just been completed in April 2016.
Finally, a 2 weeks stay in Santiago de Chile in February and a 1 week stay in Sydney in March allow us to further develop our work with R. Tiedra and to initiate a collaboration with F. Sukochev, a leading expert in non-commutative geometry and functional analysis
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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
If the progress can be counted with the number of submitted papers, then this year has been very successful: 1 paper submitted with D. Parra on discrete magnetic operators, 1 paper submitted with R. Tiedra on dynamical system, 1 review paper (54 pages) on the general approach of Levinson's theorem, 1 paper submitted with J. Derezinski on almost homogeneous Schroedinger operators. On the other hand, it is quite unfortunate because several papers have been accepted for publication but have not been published yet.
Note that some new subjects of research have been more developed than initially planed, and that some others could not progress as fast as expected. For example, the work with K. Pankrashkin on almost periodic potentials made no substantial progress during this year. However, these fluctuations are inevitable in mathematics.
Altogether, the progresses are in accordance with the initial plan of this project.
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| 今後の研究の推進方策 |
The future work will go on as planned in the original project. We expect further investigations with D. Parra on crystal lattices, and further investigations with R. Tiedra on systems with defects. A new research project has also started with A. Suzuki (Shinshu University) and R. Tiedra.
Besides our research, a rather large amount of time is spent on the dissemination of the information and on the education of the younger generations to this interdisciplinary research project. For that purpose, a master course has been given at Nagoya University during the spring semester 2015, and another one is currently delivered during the spring semester 2016. Also a weekly seminar with three 4-th year Japanese students has been organized during the entire academic year, and a new one will start very soon. These activities are our commitment for the dissemination of this research proposal and of its outcomes.
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| 次年度使用額が生じた理由 |
The leftover money is not significant and could not allow us to organize an additional trip during this fiscal year.
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| 次年度使用額の使用計画 |
The leftover money will be used for the regular activities planed in the third and final year of this project.
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