Publications

Links are on Arxiv or Google Scholar:

Preprints:

Dispersion for the wave equation in the exterior of the torus in three dimensions, with Ronald Quirchmayr preprint

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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Journal Articles:

21. Dispersive estimates for Maxwell's equations in the exterior of a sphere, with Yan-Long Fang. Journal of Differential Equations, Volume 415, 15 January 2025. paper

20. The relative trace formula in electromagnetic scattering and boundary layer operators, with Alexander Strohmaier. preprint Analysis and Partial Differential Equations. Vol 18, No. 2, 2025

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, Wiley 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

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