I am a Postdoc at the Institute of Differential Geometry, Leibniz University Hannover. Contact information can be found here.
My research is concerned with inverse problems and geometry, with tools coming from (singular) microlocal analysis. In my thesis I studied the X-ray transform in the setting of asymptotically hyperbolic manifolds, whereas more recently I have been working on inverse problems for hyperbolic equations. I am also interested in interplays between the geodesic X-ray transform on closed manifolds and higher Teichmüller theory.
Publications and Preprints:
Asymptotically Hyperbolic Manifolds with Boundary Conjugate Points but no Interior Conjugate Points.
With C. Robin Graham.
J. Geom. Anal. (2021) 31:6819–6844 arxiv
Local X-ray Transform on Asymptotically Hyperbolic Manifolds via Projective Compactification.
With C. Robin Graham.
New Zealand Journal of Mathematics, 52 (2021), 733–763. arxiv
Stability Estimates for the X-Ray Transform on Simple Asymptotically Hyperbolic Manifolds.
Pure and Applied Analysis Vol. 4 (2022), No. 3, 487–516 arxiv
Weakly nonlinear geometric optics for the Westervelt equation and recovery of the nonlinearity.
With Plamen Stefanov.
SIAM J. Math. Anal. 56 (2024), no. 1, 801–819. arxiv
The covariance metric in the Blaschke locus.
With Xian Dai.
J. Geom. Anal. 34 (2024), no. 5, Paper No. 145. arxiv
The Solid-Fluid Transmission Problem.
With Plamen Stefanov. arxiv
To appear, Transactions of the American Mathematical Society
The hyperbolic X-ray transform: new range characterizations, mapping properties and functional relations.
With François Monard and Yuzhou (Joey) Zou.
arxiv