Weyl law describes the asymptotic behavior of eigenvalues. In this talk, I will introduce the eigenvalue problem of the Schrodinger operators with singular potentials on compact manifolds. In recent works with Xiaoqi Huang (University of Maryland), we proved the pointwise Weyl laws for the Schrodinger operators with singular potentials, and constructed sharp examples on flat tori. This work extends the classical results of Avakumovic, Levitan and Hormander to Schrodinger operators. Moreover, it generalizes the 3D results of Frank-Sabin (2020) to any dimensions.

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