Research.

I am interested in problems in partial differential equations including global analysis of waves, mathematical relativity and nonlinear waves. My research involves techniques from spectral theory and microlocal analysis.

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Publications and Pre-prints

Pre-prints

with J. Wunsch. Wave propagation on rotating cosmic string spacetimes. (arXiv link)

Peer Reviewed

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

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

  3. 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)
     

  4. 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.jde.2019.09.012)
     

Thesis

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

Recent & Upcoming
Talks

For a more expansive list of talks, view my CV

1 / Conferences and Workshops

PDE Mini-School with Peter Hintz // March 2023
UNC-Chapel Hill

 

Joint Math Meetings // January 2023
Boston, MA

 

Trends in Soliton Dynamics & Singularity Formation for Nonlinear Dispersive PDEs // October 2022
Texas A&M

 

Harmonic Analysis and Waves // August 2022
University of Washington

 

Workshop on Microlocal Analysis and PDEs // July 2022
University College London

 

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

2 / Seminars and Colloquia

Ghent University // Oberlin College // University of New Mexico // Vanderbilt University // University of Kentucky 

Videos

Lecture Notes

MATH 891: Topics Course on Nonlinear Waves // Spring 2017
taught by Jason Metcalfe