包维柱教授受邀进行讲座

发布时间: 2023-12-17 15:46:00

题目：From Weyl Conjecture to Fundamental Gap Conjecture and Beyond

报告人：包维柱

时间：2023-12-15 15:00-16:00

地点：腾讯会议：656-4902-4546

报告人简介：

1995年博士毕业于清华大学，现为新加坡国立大学数学系provost讲席教授，2013年获冯康科学计算奖，2014年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，担包括SIAM Journal on Scientific Computing等多个国际期刊杂志编委。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。特别是在Bose-Einstein凝聚的数值方法及应用、高震荡色散类偏微分方程的多尺度算法和分析、无界区域上科学和工程问题的计算等方面取得了多个重要进展。

讲座摘要：

In this talk, 1 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.

主办单位：华南师范大学数学科学学院，机器学习与最优化计算实验室

协办单位：广东省青年科学家协会，广东省计算数学学会