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自由Schr\”{o}dinger方程解的几乎处处收敛问题

编辑:xyx 时间:2018年06月28日 访问次数:311

浙江大学数学科学学院九十周年院庆系列活动之四十三

题目: 自由Schr”{o}dinger方程解的几乎处处收敛问题

报告人: 张瑞祥

时间: 2018712日上午10:00-11:30

地点:  玉泉校区逸夫工商管理楼四楼  

摘要: Carleson曾提出如下的问题:对什么样的s, 自由Schrodinger方程的解会在时间趋于0时几乎处处收敛于H^s空间内的初值?此问题目前已几乎被解决 (涉及Carleson, Dahlberg-Kenig, Bourgain, Du-Guth-Li, Du-Z.的工作), 用到的方法和限制性定理方面的研究和最近Bourgain-Demeter对解耦(decoupling)定理的证明密切相关. 我们将介绍相关的工作与其中用到的方法(其中我的工作是与杜秀敏的合作工作).

研究兴趣:

Euclidean Harmonic Analysis, Especially Restriction and Kakeya Problems,

Automorphic Forms and Harmonic Analysis on Locally Symmetric Spaces

Analytic Number Theory

Incidence Geometry

教育经历:

08/2017 Ph.D. , Mathematics Department, Princeton University

Thesis Advisor: Peter Sarnak

07/2012 B.S. , School of Mathematical Sciences, Peking University

职务:

08/2018—05/2021 Van Vleck Visiting Assistant Professor, University of Wisconsin, Madison

09/2017—06/2018 Member, IAS


联系人: 王梦 mathdreamcn@zju.edu.cn



Title:  Pointwise convergence problem for the free Schr\”{o}dinger equation

Speaker:  Dr. ZHANG Ruixiang(School of Mathematics, IAS)

Time:    2018-07-12 10:00-11:30

Location:  The  4th  floor,  Sir Shaw Run Run Business Administration building,School of Mathematical Sciences, Yuquan Campus

Abstract: Carleson proposed the following problem: For which $s$, the solution of the free Schrödinger equation converges to the initial data almost everywhere when $t$ goes to $0$ and when the initial data is in $H^s$? The answer of this problem is now known up to the endpoint, which involves the work of Carleson, Dahlberg-Kenig, Bourgain, Du-Guth-Li and Du-Z. . Recent progress towards the restriction conjecture and Bourgain-Demeter's recent proof of the decoupling theorem played a crucial role in the above mentioned papers. We will survey these results and the ideas behind them (joint with Xiumin Du).

Curriculum vitae:

RESEARCH INTERESTS:

Euclidean Harmonic Analysis, Especially Restriction and Kakeya Problems,

Automorphic Forms and Harmonic Analysis on Locally Symmetric Spaces

Analytic Number Theory

Incidence Geometry

EDUCATION

08/2017 Ph.D. , Mathematics Department, Princeton University

Thesis Advisor: Peter Sarnak

07/2012 B.S. , School of Mathematical Sciences, Peking University

APPOINTMENTS

08/2018—05/2021 Van Vleck Visiting Assistant Professor, University of Wisconsin, Madison

09/2017—06/2018 Member, IAS

 

Contact Person:  WANG Meng, (mathdreamcn@zju.edu.cn)