Research on Spectra of Random Schrodinger Operators

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。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了为期5天的主要研讨会。题目是“随机算子谱理论及概率论相关领域”，参会人数约50人，其中包括7位来自国外的嘉宾，我们可以有意义的场合交流研究意见。另一个小型研讨会于2007年11月14日（星期三）至16日（星期五）在京都大学大学院人类与环境研究科举行，为期3天。本次会议的题目是“随机算子谱及相关领域”，参会人数约30人，其中包括1名来自国外的嘉宾，我们可以就研究进行密切的交流。这些讲习班讨论的专题非常丰富。主要是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。关于随机算子的话题主要是从数学的角度出发。此外，还讨论了从物理角度讨论的问题。在这些研讨会上，植木做了一个讲座，介绍了Hislop-Klopp理论在薛定谔算子的Wegner估计和随机矢量势及其在证明安德森局部化中的应用。南给讲座的一个猜想的能级统计的安德森模型。中村发表了演讲的结果半经典表征波前设置薛定谔方程。小谷了讲座建设的KdV流具有平稳性相对于时空变量由佐藤的理论动力系统的无限维格拉斯曼流形。

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.