Conferences Organized:

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. Then, I went to UC-Berkeley where I finished my Ph.D. working with Professor Daniel Tataru in 2007. My thesis topic was the asymptotic behavior of solutions to the Nonlinear Schrödinger Equation (NLSE).

From 2007-2008 and 2009-2011, 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 as a Hausdorff Center Postdoc with Professor Herbert Koch at the University of Bonn.

My research interests lie mainly in phenomenological descriptions of solutions to linear/nonlinear PDE's related to quantum mechanics and other physical models that give rise to Hamiltonian structure.

Research Topics:

Soliton existence/stability, well-posedness, scattering theory, spectral theory, Strichartz/dispersive estimates, microlocal analysis, properties of eigenfunctions on billiards, classical dynamics descriptions of PDE solutions, numerical simulations, asymptotic analysis.

Papers, Preprints and Presentations:

• 1. "Eigenfunctions For Partially Rectangular Billiards" (written with the help of Maciej Zworski). Published in Communications in Partial Differential Equations, Volume 31 (2006), 775-790.

• 2. "Fast Soliton Scattering by Delta Impurities" (with Maciej Zworski and Justin Holmer). Pubished in Communications in Mathematical Physics, Volume 274, Number 1 (2007), 187-216.

• 3. "Soliton Splitting by External Delta Potentials" (with Maciej Zworski and Justin Holmer). This is a numerical companion to the result above. 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. "Wave packet parametrices for evolutions governed by PDO's with rough symbols" (with Jason Metcalfe and Daniel Tataru). Published in Proceedings of the American Mathematical Society, Vol. 136, Number 2 (2008), 597-604.

• 5. "Strichartz estimates and local smoothing estimates for asymptotically flat Schrödinger equations" (with Jason Metcalfe and Daniel Tataru). Published in Journal of Functional Analysis, Vol. 255, Issue 6 (2008), 1497-1553.

• 6. My UC Berkeley Ph.D. Thesis supervised by Daniel Tataru. Also, here is a copy of my talk regarding the research. There will be some further details added for the resulting publications, but the main ideas are all here. Filed (2007).

• 7. "Strichartz estimates on Schwarzschild black hole backgrounds" (with Jason Metcalfe, Daniel Tataru, and Mihai Tohaneanu). Published in Communications in Mathematical Physics, Vol. 293, Number 1 (2010), 37-83.

• 8. "Counting numerical sets with no small atoms" (with Andy Miller). This article reports findings in Table 1 that follow directly from running code that computes the cardinality of numerical sets with no small atom. Similarly, in Table 2 data is recorded from running code that computes the cardinality of symmetric numerical sets with no small atom. Both codes are written in Fortran 90. To appear in Journal of Combinatorial Theory A (2010).

• 9. "An eigenfunction concentration result for polygonal billiards" (with Andrew Hassell and Luc Hillairet). Published in Communications in Partial Differential Equations, Vol. 34, Issue 5 (2009), 475-485.

• 10. "Dispersive estimates using scattering theory for matrix Hamiltonian equations". Submitted (2009).

• 11. "A class of stable perturbations for a minimal mass soliton in three dimensional saturated nonlinear Schrödinger equations". Submitted (2009).

• 12. "Existence and stability of solitons for the nonlinear Schrödinger equation on hyperbolic space" (with Hans Christianson). Published in Nonlinearity, Vol. 23 (2010), 89-106.

• 13. "A system of ODE's for a perturbation of a minimal mass soliton" (with Sarah Raynor and Gideon Simpson). Submitted (2009).

• 14. "Long time dynamics near the symmetry breaking bifurcation for nonlinear Schrödinger/Gross-Pitaevskii equations" (with Michael Weinstein). Submitted (2009).

• 15. "Dispersive estimates for the linearized quartic KdV equation and applications" (with Herbert Koch). Submitted (2010).

• 16. "Spectral analysis for matrix Hamiltonian operators" (with Gideon Simpson). Coming Soon!!

• 17. "Strichartz estimates for Schrödinger on polygonal domains" (with Matt D. Blair, G. Austin Ford and Sebastian Herr). Coming Soon!!

• Note that all finished papers above are presented in PDF format and can be found on the ArXiv's.

Links