报告题目：From Weyl conjecture to fundamental gap conjecture and beyond（从weyl猜想到基本间隙猜想及其推广）

报 告 人：包维柱教授（新加坡国立大学）

报告时间：2023年3月31日  15:00-16:00

报告地点：格物楼数统院309学术报告厅

报告简介：

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.

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，SIAM Fellow，AMS Fellow，新加坡科学院院士，本科、硕士和博士毕业于清华大学，曾获冯康科学计算奖，应邀在韩国举行的第27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，现（曾）为SIAM Journal on Numerical Analysis、SIAM Journal of Scientific Computing和IMA Journal of Numerical Analysis等国际知名期刊编委。