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【数学论坛】From Weyl conjecture to fundamental gap conjecture and beyond

发布日期:2024-04-18    点击:

北航数学论坛学术报告

From Weyl conjecture to fundamental gap conjecture and beyond

包维柱

(新加坡国立大学)

报告时间:10:30-11:30,2024-04-23(星期二)

报告地点: 沙河E-404


内容简介:In this talk, I will begin with the Weyl's law and Weyl conjecture on the asymptotics of eigenvalues of the Laplacian and Schrodinger operators (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,理学院副院长,新加坡科学院院士、SIAM Fellow(美国工业与应用数学学会院士)、 AMS Fellow(美国数学会院士),本硕博均毕业于清华大学,曾获冯康科学计算奖,应邀在韩国举行的第26届国际数学家大会上作45分钟邀请报告。包维柱教授长期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。担任SIAM Journal of Numerical Analysis等权威期刊编委。


邀请人:韩德仁


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