9月21日 王奕倩教授学术报告(数统学院)

文章作者:  发布时间: 2017-09-20  浏览次数: 10

报 告 人:王奕倩

报告题目:A dynamical system method on quasiperiodic Schrödinger operators

报告时间:2017年9月21日(周四)下午16:00

报告地点:静远楼1508报告厅

主办单位:数学与统计学院、科技处

报告人简介:

    王奕倩,南京大学教授,博士生导师.1999年在北京大学数学系获博士学位.主要研究方向:Hamiltonian动力系统与KAM理论;耦合混沌动力系统中的同步性态;拟周期薛定谔cocycle动力系统.共主持国家自然科学基金面上项目3项,作为主要成员参加国家973重大项目1项;在Duke.Math.J., J.Func.Anal. J.Differential Equations等重要期刊发表多篇论文,结果得到菲尔兹奖获得者A.Avila, ICM报告人S.Jitomirskaya和M.Schlag的肯定,被Invent.Math., J.Eur. Math. Soc.,Comm. Math. Phys.等一流杂志引用和好评;近五年应邀在美国加州理工学院、德国Oberwolfach数学所、英国剑桥大学牛顿数学所参加学术活动.

报告摘要:

    In 1958, Anderson proposed a model of Schrodinger operators(SO) for a crystal with random impurities and found that the so-called Anderson localization is the mechanism for the non-conductivity of it. Since then SO has been an active area in mathematics. From 1970s, a lot of important works on properties of spectrum and the corresponding (generalized) eigen-functions of quasi-periodic SO have been obtained, among which the occurrence of Anderson localization, the existence of phase transition and the cantor structure of spectrum are the most exciting results. In this talk we will introduce the physical background and history of spectrum theory of quasi-periodic SO. It is worthy to note, however, that most of results depend heavily on analytic conditions and are difficult to be extended to smooth situations. We then introduce a new dynamical system method on quasiperiodic SO. Based on it, we obtain a series of results only under smooth conditions. Some of them are new even in analytic topology.