Research on Spectra of Random Schrodinger Operators

随机薛定谔算子谱的研究

基本信息

批准号：
18540171
负责人：
UEKI Naomasa
金额：
$ 2.43万
依托单位：
Kyoto University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2006
资助国家：
日本
起止时间：
2006 至 2007
项目状态：
已结题

项目摘要

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.

该项目的目的是举办国际研讨会，以促进日本对随机算子的研究。主研讨会于2006年12月11日（星期一）至15日（星期五）在京都大学吉田南校区举行，为期5天。会议题目为“随机算子谱论及概率论相关领域”，参会人数约50人，其中邀请了7位国外嘉宾，为研究交流提供了有意义的机会。另一次小型研讨会于2007年11月14日（星期三）至16日（星期五）在京都大学人类环境研究科举行，为期3天。会议题目为“随机算子谱及相关领域”，参会人数约30人，其中国外嘉宾1人，可以就研究方面进行密切交流。这些研讨会讨论的主题非常丰富。这些主要是关于随机薛定谔算子和随机矩阵。此外，还讨论了金融和政治科学的各种主题。关于随机算子的主题主要是从数学角度出发的。此外，还从物理角度讨论了主题。在这些研讨会上，植木发表了关于希斯洛普-克洛普理论关于具有随机向量势的薛定谔算子的韦格纳估计的改进及其在安德森定位证明中的应用的讲座。 Minami讲授了安德森模型的能级统计猜想。中村做了关于薛定谔方程组波前半经典表征结果的演讲。小谷教授就利用佐藤无限维格拉斯曼流形上的动力系统理论构造关于时空变量具有平稳性的KdV流进行了演讲。