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I am interested in

Spectral theory of Schrödinger operators

Inverse Sturm-Liouville problems

Spectral analysis of CH equation

Spectral theory of Dirac operators

Publications & Preprints

1. (with Vishwam Khapre and Andrew Yu) Sharp bound for embedded eigenvalues of Dirac operators with decaying potentials. New York journal of mathematics, 28 (2022). PDF.

2. (with Wencai Liu) One dimensional discrete Schrödinger operators with resonant embedded eigenvalues. From Complex Analysis to Operator Theory: A Panorama: In Memory of Sergey Naboko. Cham: Springer International Publishing, 2023. 619-636. arxiv PDF.

3. (with Tao Liu) Interior inverse problem for global conservative multipeakon solutions of the Camassa-Holm equation. Journal of Differential Equations to appear, 2024, 395: 262-307. arxiv PDF.

4. (with Wencai Liu) Sharp bound for embedded eigenvalues into the essential spectrum of one dimensional discrete Schrödinger operators. In preparation.

5. (with Chuanfu Yang) Sharp spectral transition for embedded eigenvalues of perturbed periodic Dirac operators. Submitted. arxiv PDF.