1999 Fiscal Year Final Research Report Summary
Spectral and scattering theory for many particles Schrodinger operators
| Project/Area Number |
10640162
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Nagoya Institute of Technology |
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Principal Investigator |
IWASHITA Hirokazu Nagoya Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30193741)
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| Co-Investigator(Kenkyū-buntansha) |
OHYAMA Yoshiyuki Nagoya Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (80223981)
MINAMI Norihiko Nagoya Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (80166090)
TAKEMOTO Fumio Nagoya Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (50022645)
YAMAGISHI Masakazu Nagoya Institute of Technology, Faculty of Engineering, Lecturer, 工学部, 講師 (40270996)
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| Project Period (FY) |
1998 – 1999
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| Keywords | prop-p extension / Galois groups / knots / Vassiliev invariants / Seidenberg-Witten invariants / divisibility / Bender-Wu formula / Rayleigh-Schrodeinger coefficients |
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| Research Abstract |
Each of us, the investigators has researched the project from his own point of view and we have obtained the following results.
M. Yamagishi has given a survey on the Galois group of the maximal prop-p-extension (ρ a fixed prime) of a number field unramified outside a given set of places. Particulary, he has studied the presentation in terms of generators and relations, and further cohomological dimension of the Galois group.
Y. Ohyama has proved that given any knot Κ and any natural number n, there exist infinite number of knots with unknotting number one whose Vassiliev invarinats of order less than or equal to n coincide with those of Κ. Futhermore he has given another proof to the result above by using an algebraic property of the web diagrams for Vassiliev invariants.
N. Minami has obtained some result which can easily derive a theorem comcerning Hopkins' chromatic splitting conjecture. He also shows as diagram to give a note on the possibility of improving the divisibility of Seiberg-Witten invariant by Prof. M. Furuta.
With Prof. Minkyu Kwak Chonnam National University, Korea, H. Iwashita held, as a part of the research, an international meeting, the Fourth Workshop on Differential Equations at Kwangju, July of 1999. The participants were from Korea, Taiwan and Japan and their lectures and heated discussions brought great success to the meeting. The subjects of the workshop covered a wide range of fields ; spectral and scattering theory for Schrodinger operators, solvability ad asymptotic behavior of solutions to linear and nonlinear wave equations, ators, solvability of nonlinear eliptic equations, inverse problems etc. H. Iwashita edited and published the proceedings for the workshop which were also delivered to many mathematicians in the ralated fields and libraries of some foreign universities.
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