Research

Research Interests

Analysis and applications

  1. Inverse problems

    • One-dimensional scattering in non-smooth media

    • Acoustic imaging

    • Computational methods
  2. Orthogonal polynomials

  3. Combinatorial and differential geometry

  4. Complex analysis

Preprints

2022

  • Theorems of Szegö-Verblunsky type in the multivariate and almost periodic settings, 32 pages, 2022 [ArXiv version]

2021

  • Scattering on the line via singular approximation, 87 pages, 2021 [ArXiv version]

Recent Publications

2020

  • with Sophia Bugarija, Peijun Li, Guanghui Hu and Yue Zhao, Inverse scattering for the one-dimensional Helmholtz equation with piecewise constant wave speed, Inverse Problems 36 (2020), no. 7, 075008, 16pp.
    [journal link]

2019

  • Disk polynomials and the one-dimensional wave equation, Journal of Approximation Theory 244 (2019) 37-56. [journal link]

2018

  • Acoustic imaging of layered media, Journal of Computational Physics 372 (2018) 524-545. [journal link]

  • The refined impedance transform for 1D acoustic reflection data, Inverse Problems 34 (2018), no. 7, 075013, 14pp. [journal link]

  • with Guanghui Hu and Yue Zhao, Inverse medium scattering from periodic structures with fixed-direction incoming waves, Inverse Problems 34 (2018), no. 7, 075011, 18pp.
    [journal link]

  • A scattering-based algorithm for wave propagation in one dimension, Numer. Methods Partial Differential Equations, 34 (2018), no. 2, 442-450. [journal link] [ArXiv version]

2017

  • Fourier expansion of disk automorphisms via scattering in layered media, J. Fourier Anal. Appl. 23 (2017), no. 6, 1495-1516. [journal link]
    [ArXiv version].

  • with Larry Bates, A geometry where everything is better than nice, Proc. Amer. Math. Soc. 145 (2017), no. 1, 461-465. [journal link] [ArXiv version]

    Geodesics of the scattering metric are generated by hinged circles rolling in a bigger circle.

  • On the measurement operator for scattering in layered media, Inverse Problems and Imaging 11 (2017), no. 1, 87-97. [journal link]

2015

  • The Pólya-Schur problem on the unit circle, C. R. Math. Acad. Sci. Soc. R. Can. 37 (2015), no. 4, 131-141. MSC 30C15 (47B38). [journal link]

  • with Michael Lamoureux, Constructive solutions to Pólya-Schur problems, J. Funct. Anal. 269 (2015), no. 10, 3264-3281. MSC 47B33 (30C10 30C15 30H10). [ArXiv version]

  • with M. S. Tavalla, The structure of test functions that determine weighted composition operators, Sampling Theory and Applications (SampTA), 2015 International Conference on, Washington, DC, 2015, pp. 201-205. [IEEE Xplore link], [ArXiv version]

2014

  • The combinatorics of scattering in layered media, SIAM J. Appl. Math. 74 (2014), no. 4, 919-938. MSC 74J25 (35A08 35P25 35R30 76Q05 86A15). [ArXiv version]

  • A multivariate interpolation problem arising from the scattering of waves in
    layered media, Dolomites Res. Notes Approx. DRNA, 7:7-15, 2014. [journal link]