2007 Fiscal Year Final Research Report Summary
Research on Spectra of Random Schrodinger Operators
| Project/Area Number |
18540171
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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 | Kyoto University |
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Principal Investigator |
UEKI Naomasa Kyoto University, Graduate School of Human and Environmental Studies, Associate Professor (80211069)
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| Co-Investigator(Kenkyū-buntansha) |
MINAMI Nariyuki Keio University, School of Medicine, Professor (10183964)
NAKAMURA Shu The University of Tokyo, Graduate School of Mathematical Science, Professor (50183520)
SHIGEKAWA Ichiro Kyoto University, Graduate School of Science, Professor (00127234)
KOTANI Shinichi Osaka University, Graduate School of Science, Professor (10025463)
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| Project Period (FY) |
2006 – 2007
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| Keywords | Stochastic Analysis / Differential Equations / Operator Theory / Mathematical Physics / Random Schrodinger Operators / Random Matrix / Spectrum / Schrodinger Operators |
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| Research Abstract |
The aim of this project is to held international workshops to promote the research on random operators in Japan. The main workshop was held for 5 days from 2006 December 11 (Monday) to 15 (Friday) at Kyoto University, Yoshida South Campus. The title was "Spectral Theory of Random Operators and Related Fields in Probability Theory", the amount of the participants were about 50 including 7 guests invited from abroad, and we could have meaningful occasions for exchanging ideas for researches. Another smaller workshop was held for 3 days from 2007 November 14 (Wednesday) to 16 (Friday) at Kyoto University, Graduate School of Human and Environmental Studies. The title was "Spectra of Random Operators and Related Fields", the amount of the participants was about 30 including 1 guest from abroad and we could have close communications on researches. The topics treated in these workshops were very substantial. Those were mainly on random Schrodinger operators and random matrices. Moreover various topics on financial and political sciences were also treated. The topics on random operators were mainly from mathematical viewpoints. Moreover the topics from physical viewpoints were also treated. In these workshops, Ueki gave a lecture on a refinement of Hislop-Klopp theory on the Wegner estimate for Schrodinger operators with random vector potentials and its applications to the proof of the Anderson localization. Minami gave lectures on a conjecture on energy level statistics for the Anderson model. Nakamura gave a lecture on the results on the semi-classical characterization of the wave front set of Schrodinger equations. Kotani gave a lecture on the construction of the KdV flow having stationarity with respect to the space-time variables by Sato's theory on the dynamical system on the infinite dimensional Grassmanian manifolds.
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[Presentation] KdV-flow and Floquet exponents2006
Author(s)
Shin-ichi, Kotani
Organizer
Workshop "Spectral Theory of Random Operators and Related Fields in Probability Theory"
Place of Presentation
Kyoto University, Yoshida South Campus
Year and Date
2006-12-12
Description
「研究成果報告書概要(欧文)」より
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