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Research

Research Interests

My research lies in the broad area of applied mathematics and analysis of partial differential equations. Of particular interest are questions related to the mathematical aspects of materials science, such as cloaking, metamaterials, and complex media; linear passive systems; (inverse) scattering theory; and nonlinear optics.

Publications and Preprints

  • On the optimality of broadband scattering estimates for a passive transformation optics cloak, in preparation.
  • (with M. Vogelius) On the existence of positive nonlinear transmission eigenvalues in the second-harmonic generation process, in preparation.
  • (with F. Cakoni, M. Lassas and M. Vogelius) On the lack of external response of nonlinear media in the second-harmonic generation process, submitted arXiv:2401.00998
  • On the distribution of Born transmission eigenvalues in the complex plane, Asymptot. Anal.,136, No. 1, pp. 27-60, 2024.   journal link | arXiv
  • (with F. Cakoni and M. Vogelius) Far field broadband approximate cloaking for the Helmholtz equation with a Drude-Lorentz refractive index, J. Math. Pures Appl., 182, pp. 285-318, 2024..   journal link | arXiv
  • On the optimal analytic continuation from discrete data, Houst. J. Math., 48, No. 2, pp. 281–293, 2022.   journal link | arXiv
  • (with D. Harutyunyan) On the extreme rays of the cone of 3×3 quasiconvex quadratic forms: extremal determinants vs. extremal and polyconvex forms, Arch. Ration. Mech. Anal., 244, pp. 1-25, 2022.   journal link | arXiv
  • (with Y. Grabovsky) On the feasibility of extrapolation of the complex electromagnetic permittivity function using Kramers-Kronig relations, SIAM J. Math. Anal., 53, No. 6, pp. 6993–7023, 2021.   journal link | arXiv
  • (with Y. Grabovsky) On the commutation properties of finite convolution and differential operators II: sesquicommutation, Results Math, 76, No. 3, Article 111, 2021.    journal link | arXiv
  • (with Y. Grabovsky) On the commutation properties of finite convolution and differential operators I: commutation, Results Math, 76, No. 3, Article 112, 2021.    journal link | arXiv
  • (with Zh. Avetisyan and D. Harutyunyan) Rigidity of a thin domain depends on the curvature, size, and boundary conditions, Appl. Math. Opt., 84, pp. 3229–3254, 2021.   journal link | arXiv
  • (with Y. Grabovsky) Optimal error estimates for analytic continuation in the upper half-plane, Commun. Pure Appl. Math, 74, No. 1, pp. 140-171, 2021.    journal link | arXiv
  • (with Y. Grabovsky) Explicit power laws in analytic continuation problems via reproducing kernel Hilbert spaces, Inverse Problems, 36, No. 3, pp. 035001-035023, 2020.    journal link | arXiv
  • (with J. J. L. Velázquez) Hopf Bifurcation in structural population models, Math. Methods Appl. Sci., 39, No. 18, pp. 5258 – 5280, 2016.    journal link | arXiv
  • (PhD dissertation) Quantification of Stability of Analytic Continuation with Applications to Electromagnetic Theory, Temple University ProQuest Dissertations Publishing, 2021.   link