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.

Publications

Peer-Reviewed

• 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, 2020 Canceled 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