I study, broadly, differential geometry, geometric analysis, and PDEs. I am particularly interested in the geometry of submanifolds in conformal geometry, and in related questions in geometric PDEs on singular domains (such as domains with corners). I am interested in connections of all these subjects to physics, especially via the AdS/CFT correspondence. I have various ongoing projects that are suitable for participation by graduate students or undergraduates.

Here is a current list of my published and submitted papers. I am preparing several more.

- (With Matthew J. Gursky and Aaron J. Tyrrell) Self-dual and even Poincaré-Einstein metrics (submitted)
- (With Jeffrey S. Case, Yueh-Ju Lin, Cheikh Birahim Ndiaye, and Paul Yang) A fourth-order Cherrier-Escobar problem with prescribed corner behavior on the half-ball (submitted)
- (With Matthew J. Gursky and Aaron J. Tyrrell) "Renormalized volume of minimally bounded regions in asymptotically hyperbolic Einstein spaces"
(arXiv); Advances in Theoretical and Mathematical Physics
**26**(9), 3081-3123 (2022). - (With Sun-Yung Alice Chang and Paul Yang) "Scattering on singular Yamabe spaces"(arXiv);
Revista Matemática Iberoamericana
**38**(7), 2153-2184 (2022) - "Extrinsic curvature and conformal Gauss-Bonnet for four-manifolds
with corner" (arXiv); Pacific Journal of Mathematics
**314**(2), 411-424 (2021) - "Formal
theory of cornered asymptotically hyperbolic Einstein metrics"
(arXiv); Journal of
Geometric Analysis
**29**(3), 1876-1928 (2019). - "Exponential
map and normal form for cornered asymptotically hyperbolic metric"
(arXiv); Transactions
of the AMS
**372**, 4391-4424 (2019).