学术报告

报告题目：From Weyl conjecture to fundamental gap conjecture and beyond

主讲人：包维柱教授（新加坡国立大学）

时间：2021年12月21日，15:00-16:00

腾讯会议ID：143 355 654

内容简介：In this talk, I will begin with the Weyl's law andWeyl conjecture on the asymptotics of eigenvalues of theLaplacian and Schrodinger operators (LO/SO) on bounded domains with Dirichlet boundary condition. Based on our recent numerical results by using a spectral method, Ireport some information on the reminder in the Weyl conjecturefor 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 – differencebetween 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：Professor Weizhu Bao is currently a professor at Department of Mathematics, National University of Singapore (NUS). He got his PhD from Tsinghua University in 1995 and afterwards he had postdoc and faculty position at Tsinghua University, Imperial College in UK, Georgia Institute of Technology and University of Wisconsin at Madison in USA. He joined NUS as an Assistant Professor in 2000 and was promoted to Professor in 2009. 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 His research interests include numerical methods for partial differential equations, scientific computing/numerical analysis, and computation for problems from physics, chemistry, biology and engineering sciences. He was on the Editorial Board of SIAM Journal on Scientific Computing during 2009-2014. 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. In 2021, Prof Bao has been elected as a Fellow of the American Mathematical Society for his contributions to numerical analysis, in particular the numerical solution of partial differential equations and their applications.

欢迎各位老师和同学准时参加！