Research Interests

I am interested in problems in partial differential equations, spectral theory, microlocal analysis, global analysis, and nonlinear waves.

See my research statement for a more detailed discussion of my work.

Publications and Pre-prints

  1. with J. Wunsch. Solvability of the wave equation on rotating cosmic string backgrounds. In progress. (preprint available upon request)
     

  2. with J. Wunsch. Mode Solutions to the wave equation on a rotating cosmic string background. Proceedings of the AMS. To appear(arXiv link)
     

  3. with J. Wunsch. Generalized Price's law on fractional-order asymptotically flat stationary spacetimes. Mathematical Research Letters. To appear (arXiv link)
     

  4. The effect of metric behavior at spatial infinity on pointwise wave decay in the asymptotically flat stationary setting. American Journal of Mathematics. To appear. (arXiv link)
     

  5. with J. Metcalfe. Global existence for systems of quasilinear wave equations in (1+4)-dimensions. Journal of Differential Equations. 2020. (https://doi.org/10.1016/j.hde2019.09.012)
     

  6. Wave decay in the asymptotically flat stationary setting. 2019, 155 pages. Available from ProQuest Dissertations and Theses Global. (2296357806)

Selected Talks

Invited 
  • Trends in Soliton Dynamics & Singularity Formation for Nonlinear Dispersive PDEs (October 2022)
    Texas A&M
     

  • Harmonic Analysis and Waves (August 2022)
    University of Washington
     

  • Analysis Seminar (May 2022)
    University of New Mexico (delivered remotely)
     

  • Partial Differential Equations Seminar (October 2021)
    Vanderbilt University
     

  • International Congress on Mathematical Physics Young Researchers Symposium (July 2021)
    Geneva, Switzerland (delivered remotely)
     

  • Analysis and PDE Seminar (May 2021)
    University of Kentucky (delivered remotely)

     

  • Canadian Mathematical Society Summer Meeting (June 2020)
    Ottowa, Canada - cancelled due to COVID

     

  • Microlocal Analysis Seminar (October 2019)
    Mathematical Sciences Research Institute

     

  • Harmonic Analysis and Differential Equations Seminar (October 2019)
    University of California - Berkeley

     

  • Analysis and Partial Differential Equations Seminar (March 2019)
    University of Kentucky

     

  • Spectral and Scattering Theory Seminar (October 2018)
    Purdue University
     

  • AMSI-ANU Workshop on Microlocal Analysis (March 2018)
    South Durras, Australia 

Selected Other Talks

  • Workshop on Microlocal Analysis and PDEs (July 2022)
    University College London
     

  • Analysis and Geometry of Nonlinear Evolution Equations AMS Speciall Session (January 2019)
    Joint Mathematics Meetings, Baltimore, MD

     

  • Texas Analysis and Mathematical Physics Symposium (October 2018)
    Baylor University

Videos

Notes