Professor Weizhu Bao was invited to give a lecture

发布时间: 2023-12-18 20:50:00

Topic： From Weyl Conjecture to Fundamental Gap Conjecture and Beyond

Speaker：Weizhu Bao

Time：2023-12-15 15:00-16:00

Tencent Meeting ID： 656-4902-4546

Introduction：

    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.

Organizer

School of Mathematical Sciences, South China Normal University, Machine Learning and Optimization Computing Laboratory

Co-organizers

Guangdong Young Scientists Association

Guangdong Computational Mathematical Society