| 研究課題/領域番号 |
16K05051
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| 研究機関 | 北海道大学 |
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研究代表者 |
セッテパネーラ シモーナ 北海道大学, 理学研究院, 准教授 (40721890)
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| 研究期間 (年度) |
2016-04-01 – 2019-03-31
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| キーワード | Discriminantal arrang. / braid groups / Grassmannian / Plucker embedding / fundamental groups / Gale transform |
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| 研究実績の概要 |
During this year of research the Principal Investigator (P.I.) worked to the project with A. Libgober and completed a paper "Strata of discriminantal arrangements" which is presently submitted and under review. In particular the P.I. and the co-author were able to give a complete description of combinatorics of 2 strata of Discriminantal Arrangement. This allowed to involve in the project two master students of the applicant, S. Yamagata and S. Sawada with whom the P.I. wrote a paper. In this paper the result obtained in the paper with A. Libgober is connected to the study of hypersurfaces in Grassmannian, showing that special conbinatorics property of intersection lattice of Discriminantal arrangements describe hypersurfaces in the Grassmannian when view as projective variety. Moreover it has been possible to finally give a conjecture on the complete intersection lattice of Discriminantal arrangement obtaining also some partial results on combinatorics of higher strata of Dicsriminantal arrangement. Moreover during this year the P.I. studied jointly with one of her student possible applications of their results about Grassmannian to the study of protein folding.
Moreover the P.I. finished a paper with a second co-author, P. Bailet, related to the study of rank 2 intersection lattice of any arrangement.
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| 現在までの達成度 (区分) |
現在までの達成度 (区分)
2: おおむね順調に進展している
理由
The project started with the idea of study higher dimensional Braid groups, proved to be much more interesting than expected. Indeed it turned out to be related to several very important mathematical objects both in combinatorics and algebraic geometry. Indeed the research lead to the study of the combinatorics of Discriminantal arrangement that is a whidely studied object in algebra, in combinatorics and in algebraic geometry. The results obtained in the project allowed to finally make a conjecture on the complete description of intersection lattice of Discriminantal arrangement. The P.I. jointly with his co-researcher A. Libgober and her students has been able to prove some partial result toward the final proof of the conjecture.
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| 今後の研究の推進方策 |
The future research of the P.I. will mainly focus on the proof of conjecture about intersection lattice of Discriminantal arrangement. In particular to generalize the result they got on the existence of m-strata of multimplicity m+1. Moreover the P.I. jointly with her student S. Yamagata and co-researcher from Chemistry Department of Hokkaido University, will investigate the problem of proteint folding. In particular the main idea is to understand possible connections between very non generic configurations of plane in the space that lead to special combinatorics for Discriminantal arrangement and special configurations that caraterize protein folding. Moreover the P.I. is planning to continue studies with P. Bailet that already lead to a paper accepted for publication
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| 次年度使用額が生じた理由 |
Next year money will be used mainly for travel expenses. Those travel will be necessary to meet co-authors in order to work together to the planned reseacrh plan. Both P.I. travel to reach co-authors in their own Countries and support for co-authors to come to Hokkaido University are plannes.In addition to that trip to participate to conferences to give talks on the research achievement are planned.
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| 次年度使用額の使用計画 |
Next year money will be used mainly for travel expenses. A trip to Europe is planned from April 21th to June 28th. In this period the P.I. will meet both co-authors P. Bailet in Bremen (Germany) and A. Libgober in Pisa (Italy). In this period attendance of a Conference in Pisa is planned. Author will give a seminar in this occasion. P.I. also planned to buy several books needed for her research.
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