学术报告

【online】From Weyl conjecture to fundamental gap conjecture and beyond

发布人:发布时间: 2020-09-25

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Series Talks on Optimal Transportation Problems, PDEs and Their Applications in Image Processing

“最优运输问题、PDE和在图像处理中的应用”系列学术报告

 

题目From Weyl conjecture to fundamental gap conjecture and beyond

 

报告人Professor Weizhu BaoDepartment of MathematicsNational University of Singapore 


报告时间:2020年1013日上午10:00

 

方式 腾讯会议   ID:  292 608 385 (密码:456123

 

摘要In this talk, I will begin with the Weyl's law and Weyl conjecture on the asymptotics of eigenvalues of the Laplacian operator and the Schrodinger operator (LO/SO) on bounded domains with Dirichlet boundary condition. Based on our recent numerical results by using a spectral method, I report some information on the reminder in the Weyl conjecture for the LO/SO. In addition, a generalized Weyl's law for the fractional Schrodinger operator (FSO) is proposed. Then I review the fundamental gap conjecture – difference between the first two smallest eigenvalues -- of the LO/SO. Again, based on our recent asymptotic and numerical results, we propose a gap conjecture on the fundamental gap of the FSO. In addition, different gaps of eigenvalues of the FSO are discussed and the ``unfolding'' gaps statistics of FSO is reported. Finally, fundamental gaps on energy and chemical potential of the Gross-Pitaevskii equation are studied asymptotically and numerically.

 

报告人简介包维柱,新加坡国立大学数学系教授,新加坡国立大学数学系研究生委员会主任。1992年毕业于清华大学数学系,获学士学位。1995年毕业于清华大学,获硕士和博士学位。2013年获得第十届冯康科学计算奖,在第26届国际数学家大会(2014年)上作45分钟邀请报告。包维柱教授主要从事科学与工程计算研究,主要工作涉及偏微分方程数值方法及其在量子物理、流体和材料中的应用。


邀请人:杨孝平 老师