Research

Preprints and publications

1. Witten instanton complex and Morse-Bott inequalities on stratified pseudomanifolds  (with G. Jayasinghe and X. Yu)

2. Exponential localization of 2d Magnetic Schrödinger eigenfunctions via Brownian flux 

3. On the localization of eigenfunctions of the magnetic Laplacian (with J. Ovall, R. Reid, and S. Steinerberger)

   • To appear, Reports on Mathematical Physics

4. The Wave Trace on Asymptotically Complex Hyperbolic Manifolds

   • Submitted, August 2023

5. Self-adjointness criteria and self-adjoint extensions of the Laplace-Beltrami operator on $\alpha$-Grushin manifolds (with I. Beschastnyi )

   • Submitted, May 2023

6. Magnetic Schrodinger operators and landscape functions. (with J. Hoskins and S. Steinerberger)

   • Communications in PDE. DOI: 10.1080/03605302.2023.2292992

7.  The Calderon problem for the fractional Dirac Operator. (with G. Uhlmann)

   • Accepted, Mathematical Research Letters.

8. Sub-Riemannian limit of the differential form heat kernels of contact manifolds.  (with P. Albin)

   • International Mathematics Research Notices. Volume 2022, Issue 8, April 2022, Pages 5818–5881.

Supported Publications

1. McMullen's Eigenvalue Algorithm for the Hausdorff Dimension of Complex Kleinian Groups  (J. Linden and X. Wu)

   • Rose-Hulman Undergraduate Math Journal, Volume 24, Issue 2, November 27 2023