报告人：Weizhu Bao (新加坡国立大学)

时间：2021年12月09日15:00开始

腾讯会议ID：726 389 826  ( 密码：5820)

摘要：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.

简介:Professor Weizhu Bao （包维柱） is currently a Professor at Department of Mathematics and Vice Dean for Graduate Studies and Academic Affair of Faculty of Science (FoS), National University of Singapore (NUS). He got his PhD from Tsinghua University in 1995 and afterwards he had postdoc and faculty positions at Tsinghua University, Imperial College in UK, Georgia Institute of Technology and University of Wisconsin at Madison in USA. He had been appointed as the Provost's Chair Professorship at NUS during 2013 -- 2016. His research interests include numerical methods for partial differential equations, scientific computing/numerical analysis, analysis and computation for problems from physics, chemistry, biology and engineering sciences. He was awarded the Feng Kang Prize in Scientific Computing by the Chinese Computational Mathematics Society in 2013. He has been invited to give plenary and/or invited talks in many international conferences including the Invited Speaker at the International Congress of Mathematicians (ICM) in 2014.  He was elected the fellow of the American Mathematical Society (AMS) of 2022.

邀请人：刘磊

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