Publications 


   Links are on Arxiv or Google Scholar: 

Not all papers are on the Arxiv. This list also has links to the published copies when the manuscript has been made open access.

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Preprints:

21. Dispersive estimates for Maxwell's equations in the exterior of a sphere, with Yan-Long Fang. preprint

Journal Articles: 

20. The relative trace formula in electromagnetic scattering and boundary layer operators, with Alexander Strohmaier. preprint Analysis and Partial Differential Equations (to appear). 

19. Observability for Schrodinger Equations with Quadratic Hamiltonians. Partial Differential Equations and Applications. (2023). paper 

18. The Birman-Krein formula for differential forms and electromagnetic scattering, with Alexander Strohmaier in Bulletin des Sciences Mathematiques (2022).  paper

17. Analytic properties of heat equation solutions and reachable sets with Alexander Strohmaier. Mathematische Zeitschrift, (2022).  paper

16. A relative trace formula in obstacle scattering, with Florian Hanisch and Alexander Strohmaier. In Duke Mathematical Journal, (2022) . preprint

15. Recovery of a Lame Parameter from Displacement fields in Nonlinear Elasticity with Hugo Carrillo-Lincopi, Inverse and Ill posed problems, (2021). paper 

14. Geometric obstacle scattering at low energy, with Alexander Strohmaier. Communications in Partial Differential Equations (2020).  some typos, paper

13. Rank Optimality for the  Burer-Monteiro factorization. with Irene Waldsburger.  Siam Journal of Optimization, (2020). paper

12. Low regularity ray tracing for wave equations using Gaussian beams. Rocky Mountain Journal of Mathematics, Vol 9, No. 3 (2019)  paper, preprint

11. Unique determination of sound speeds for coupled systems of semi-linear wave equations Indagationes Mathematicae Vol 30, No 5 (2019) pp 904-919. paper 

10. Asymptotics for optimal design problems for the Schrodinger equation with a potential with Ekaterina Merkurjev, Journal of Optimisation, open access online (2018) paper

9. Recovery of Coefficients for the Acoustic Wave equation from Phaseless measurements with Joonas Ilmavirta. (CMS) Comm. Math. Sciences Vol. 16, No. 4 (2018), pp. 1017-1041 paper

8. Phaseless Stability for Helmholtz: Communications in Mathematical Sciences (2018) paper

7. A Deterministic Optimal Design Problem for the Heat Equation, with Heiko Gimperlein Siam Journal of Control Theory 2017 paper

6. Lower Resolvent Bounds and Lyapunov Estimates, with Semyon Dyatlov. Applied Mathematics Research Express 2016 paper

5. Stability Analysis in Magnetic Resonance Elastography II, with Heiko Gimperlein Journal of Mathematical Analysis and Applications. 2016 paper

4. Stability Analysis for Magnetic Resonance Elastography, with Hai Zhang and Habib Ammari, Journal of Mathematical Analysis and Applications 2015 paper

3. Stable determination of X-ray transforms of time dependent potentials from the dynamical Dirichlet-to-Neumann map Comm. Partial Differential Eq. 2014 preprint

2. Isospectral Periodic Torii in Dimension 2 Annales de L'Institut Henri Poincare (C) 2014 paper

1. A Parametrix Construction for the Wave Equation with Low Regularity Coefficients Using a Frame of Gaussians Communications in Mathematical Sciences 2011. paper

Popular Science Articles:

1. Study of the Joukowski transformation for medical imaging applications, with Teke Xu and Samuel Galanakis. Periodiek Magazine. 

Refereed Conference Proceedings:

PhD Thesis:

A Parametrix Construction for Low Regularity Wave Equations and Spectral Rigidity for Two Dimensional Periodic Schrodinger Operators Thesis 2012

Other selected works:

Stability for Time Dependent X-ray Transforms and Applications preprint (explanation of ray transforms not intended for publication)

Approximation of the nonlinear water hammer problem by a Lax-Wendroff finite difference scheme, with Hugo Carrillo-Lincopi and Teke Xu. preprint (part of the thesis by Xu)