Research & Professional Development
I am interested in the existence and stability of nonlinear waves in nonlocal dispersive equations, especially the Fractional Nonlinear Schrödinger Equation (fNLS) and bidirectional Whitham water wave models. I also use numerical methods to compute bifurcations and spectra, with the goal of motivating and verifying theoretical results.
Nondegeneracy and Stability of Antiperiodic Bound States for Fractional Nonlinear Schrodinger Equations
With Mathew A. Johnson.
Journal of Differential Equations, 2019. (arXiv:1606.06213)
Existence of a highest wave in a fully dispersive two-way shallow water model
With Mats Ehrnström and Mathew A. Johnson.
Archive for Rational Mechanics and Analysis, 2019. (arXiv:1610.02603)
Numerical Bifurcation and Spectral Stability of Wavetrains in Bidirectional Whitham Models
With Mathew A. Johnson.
Studies in Applied Mathematics, 2018. (arXiv:1710.09950)
I am an inductee of the Peach '18 Project NExT cohort!
Recent Conferences / Workshops Attended
SIAM Conference on Nonlinear Waves and Coherent Structures (NWCS20), July 27-30, 2020Canceled due to COVID-19
- SIAM Conference on Analysis of Partial Differential Equations (PD19), December 11-14, 2019
- Miami University Forty-Seventh Annual Mathematics Conference: Differential Equations and Dynamical Systems and their Applications, September 20-21, 2019
- MAA MathFest 2019 / Project NExT, July 31-August 3, 2019
- KUMUNU Conference on PDE, Dynamical Systems, and Applications, April 27-28, 2019
- Rose-Hulman Undergraduate Math Conference, April 19-20, 2019
- 83rd Midwest PDE Seminar, March 30-30, 2019
- Joint Math Meetings 2019 / Project NExT, January 15-19, 2018
- Indiana MAA Section Meeting, October 12-13, 2018
- MAA MathFest 2018 / Project NExT, July 29-August 4, 2018
- Joint Math Meetings 2018, January 10-13, 2018
- Creighton Department of Mathematics Conference for Undergraduates, October 6-7, 2017
- SIAM Conference on Applications of Dynamical Systems (Snowbird), May 21-25, 2017
- Rocky Mountain Conference on Partial Differential Equations, May 18-19, 2017
- KUMUNU Conference on PDE, Dynamical Systems and Applications 2017, April 21-23, 2017
- The Tenth IMACS Conference on Nonlinear Evolution Equations, March 29-April 1, 2017
- Annual Meeting of SIAM Central States Section, September 30-October 2, 2016
- SIAM Conference on Nonlinear Waves and Coherent Structures, August 8-11, 2016