中科院数学与系统科学研究院

数学研究所

偏微分方程研讨班

报告人：张城 博士 (University of Rochester)

题  目：Weyl Laws of Schrodinger operators on manifolds

时  间：2021.11.12（星期五）, 10:00-11:00

地  点：数学院南楼N204腾讯会议：737 926 522  

摘  要：Weyl law describes the asymptotic behavior of eigenvalues. I will introduce the eigenvalue problem of the Schrodinger operators with singular potentials on compact Riemannian manifolds. In recent works with Xiaoqi Huang (Universityof Maryland), we proved the pointwise Weyl laws for the Schrodinger operators with critically singular potentials, and showed that they are sharp by constructing explicit examples on flat tori. This work extends recent 3D results of R.L. Frank (Caltech) andSabin (University of Paris-Saclay) to any dimensions.