My advisor is Dr. Mathew Johnson, and I am interested in 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.
- Numerical Bifurcation and Spectral Stability of Wavetrains in Bidirectional Whitham Models, arXiv:1710.09950. With Mathew A. Johnson. Submitted for publication.
- Existence of a highest wave in a fully dispersive two-way shallow water model, arXiv:1610.02603. With Mats Ehrnström and Mathew A. Johnson. Submitted for publication.
- Nondegeneracy and Stability of Antiperiodic Bound States for Fractional Nonlinear Schrodinger Equations, arXiv:1606.06213. With Mathew A. Johnson. Submitted for publication.
Conferences / Workshops Attended
- 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
- Gene Golub Summer School on Stochastic Differential Equations and Wave Propagation, July 25-August 5, 2016
- KUMU PDE, Dynamical Systems, and Applications, April 23-24, 2016
- AMS Central Spring Sectional Meeting, March 14-15, 2015
- KUMU PDE, Dynamical Systems, and Applications, April 18-19, 2015
- Stability of Solitary Waves Summer School & Workshop, May 19-30, 2014
- First Central Region Conference on Numerical Analysis and Dynamical Systems, May 3-5, 2013
- Calculus III - MATH 127 Lab (Spring 2017)
- Calculus III - MATH 127 Lab (Fall 2016)
- Calculus II - MATH 126 Lab (Spring 2016)
- Calculus II - MATH 126 (Fall 2015)
- Calculus II - MATH 122 Lab (Spring 2015)
- Calculus I - MATH 121/197 Enhanced (Fall 2014)
- Calculus I - MATH 121 Lab (Spring 2014)
- Business Calculus I - MATH 115 (Fall 2012, Spring/Fall 2013)
- Analysis Qual Prep Seminar (Fall 2013 - Spring 2014)
Wiimote PlanimeterTo show students an interesting application of Green's Theorem (my second most favorite theorem, a very close second after the Mean Value Theorem), I wrote some software that uses a Nintendo Wiimote to find the area of a real-life region based on the well-known formula
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3D-Printed ObjectsThanks to Dr. Estela Gavosto, I have had the opportunity to learn how to use a 3D printer to create tangible representations of mathematical surfaces.
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