Spectral and scattering theory for many particles Schrodinger operators
Project/Area Number  10640162 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Basic analysis

Research Institution  Nagoya Institute of Technology 
Principal Investigator 
IWASHITA Hirokazu Nagoya Institute of Technology, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30193741)

CoInvestigator(Kenkyūbuntansha) 
YAMAGISHI Masakazu Nagoya Institute of Technology, Faculty of Engineering, Lecturer, 工学部, 講師 (40270996)
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)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,600,000 (Direct Cost : ¥2,600,000)
Fiscal Year 1999 : ¥1,200,000 (Direct Cost : ¥1,200,000)
Fiscal Year 1998 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  propp extension / Galois groups / knots / Vassiliev invariants / SeidenbergWitten invariants / divisibility / BenderWu formula / RayleighSchrodeinger coefficients / RayleighSchrodinger係数 / 軸対称 / prop extension / ガロア群 / 結び目 / Vassiliev不変量 / SeibergWitten不変量 
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 proppextension (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 SeibergWitten 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.

Report
(4results)
Research Output
(9results)