Professional:

About Me:

I received my undergraduate degree from the University of Oklahoma in 2002, where I wrote an undergraduate thesis on Numerical Semigroups with Professor Andy Miller. However, when I came to Berkeley in the Fall of 2002, I had developed an interest in studying Analysis and PDE's after doing a good deal of work in physics as an undergrad. There, I finished my Ph.D. working with Professor Daniel Tataru. My thesis topic was the asymptotic behavior of solutions to the Nonlinear Schrodinger Equation (NLSE). From 2007 to 2011, I will be at Columbia University as a National Science Foundation Postdoctoral Research Fellow working with Professor Michael Weinstein. However, I am spending the academic year 2008-2009 visiting Professor Herbert Koch at the University of Bonn.

Research:

My interests lie mainly in phenomenological studies of nonlinear dispersive PDE's related to physics. Hence, with my collaborators I study soliton existence/stability theory, scattering, spectral theory, Strichartz/dispersive estimates, microlocal analysis, billiard problems, classical dynamics descriptions of PDE solutions, numerical simulations and asymptotic analysis.

Papers and Presentations:

• 1. A preprint of an article entitled "Eigenfunctions For Partially Rectangular Billiards" written with the help of Maciej Zworski can be found here in PDF. Published in Communcations in Partial Differential Equations, Volume 31 (2006), 775-790.
• 2. A preprint of an article entitled "Fast Soliton Scattering by Delta Impurities" worked on with Maciej Zworski and Justin Holmer can be found here in PDF. Pubished in Communications in Mathematical Physics, Volume 274, Number 1 (2007), 187-216.
• 3. A numerical companion to the result above with Maciej Zworski and Justin Holmer entitled "Soliton Splitting by External Delta Potentials" can be found here in PDF. If you are interested in the numerical methods, feel free to e-mail me. Published in the Journal of Nonlinear Science, Volume 17, Number 4 (2007), 349-367.
• 4. A preprint of an article entitled "Wave packet parametrices for evolutions governed by PDO's with rough symbols" written with Jason Metcalfe and Daniel Tataru can be found here in PDF. Published in Proceedings of the American Mathematical Society, Vol. 136, Number 2 (2008), 597-604.
• 5. A preprint of an article entitled "Strichartz estimates and local smoothing estimates for asymptotically flat Schrödinger equations" written with Jason Metcalfe and Daniel Tataru can be found here in PDF. Published in Journal of Functional Analysis, Vol. 255, Issue 6 (2008), 1497-1553.
• 6. A copy of my thesis is posted here in PDF. Also, here is a copy of my talk notes regarding the research in PDF. There will be some further details added for the published version, but the main ideas are all here. Filed, 2007.
• 7. A preprint of an article entitled "Strichartz estimates on Schwarzschild black hole backgrounds" written with Jason Metcalfe, Daniel Tataru, and Mihai Tohaneanu can be found here in PDF. Submitted, 2008.
• 8. A preprint of an article entitled "Counting numerical sets with no small atoms" written with Andy Miller can be found here in PDF. Submitted, 2008.
• 9. A preprint of an article entitled "An eigenfunction concentration result for polygonal billiards" written with Andrew Hassell and Luc Hillairet can be found here in PDF. Published in Communications in Partial Differential Equations, Vol. 34, Issue 5 (2009), 475-485.
• 10. A preprint of an article entitled "Dispersive estimates using scattering theory for matrix Hamiltonian equations" can be found here in PDF. Submitted, 2009.
• 11. A preprint of an article entitled "A class of stable perturbations for a minimal mass soliton in three dimensional saturated nonlinear Schrödinger equations" can be found here in PDF. Submitted, 2009.
• 12. A preprint of an article entitled "Existence and stability of solitons for the nonlinear Schrödinger equation on hyperbolic space" written with Hans Christianson can be found here in PDF. Submitted, 2009.
• 13. A preprint of an article entitled "A system of ODE's for a perturbation of a minimal mass soliton" written with Sarah Raynor and Gideon Simpson can be found here in PDF. Submitted, 2009.
• Note that all finished papers above can be found on the ArXiv's.

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