| 研究実績の概要 |
This year has been very special, with the Covid 19 pandemic. It has not been possible to do any trip for collaboration, invite any colleague, or attend any real conference. The research activities have been adapted accordingly, and have been centered on three topics:
1) With R. Tiedra and L. Zhang, we completed some investigations on 2 dimensional Schroedinger operators, concentrating on the 0-energy threshold.
New formulas have been exhibited in this context, which lead to new index theorems in scattering theory. The 2D setting is known to be more complicated than the 1D or 3D case. The results of these investigations have been submitted for publication.
2) With Q. Sun, we performed some bibliometric investigations on a database about publications in mathematics. For a long time, we wanted to test how much information can be extracted from such a database, and the traveling restrictions have provided a good opportunity for this research. The evolution of several quantifiers about publications in mathematics, but also some comparisons between publications produced in different countries (or in collaboration) have been studied. The outcomes have been gathered in an accepted publication.
3) With Professor Miyoshi (RIKEN and Kyoto University) and with Q. Sun we have started a collaboration related to the propagation of epidemics. Our approach uses data assimilation and graph theory, and preliminary results have already been presented at some online conferences or seminars. Two papers are in preparation, and these developments are quite exciting.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
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理由
Because of the Covid 19 pandemic, the research program has been adapted. We have performed as much research as possible in this complicated context. Fortunately, research in mathematics does not necessitate big investments, which means that one can be more flexible and update the research directions according to the context. This is what we have done this year, and the outcomes are still ample.
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| 今後の研究の推進方策 |
Because of the pandemic, this project has been extended for one more year. The collaboration about the propagation of epidemics will continue, and an additional project about crystal lattices will be completed in the summer 2021. If the conditions are met, we hope to finish the investigations on surface states, concentrating on the algebraic side of the problem (the analytic part being already solved). Finally, a project entitled "Decay estimates for unitary representations with applications to self-adjoint and unitary operators" should also be completed in the second half of 2021. Clearly, research outcomes will depend on the worldwide developments of the coronavirus outbreak.
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