Thank you for visiting my webpage. I am currently a postdoctoral research associate in the mathematics department at the University of Arizona. I have worked previously at the International School for Advanced Study (ISAS/SISSA) in Trieste, Italy and at the University of Michigan.
I think of myself as an applied analyst; I work on problems of an analytical nature that arrise in diverse areas of mathematics and the physical sciences.
One of my principle interest is integrable systems theory. I use the tools of integrability to study problems in nonlinear dispersive PDE—particularly soliton stabiliy and small dispersion limits of solutions—as well as problems in random matrix theory, and random growth processes through their connection with orthogonal polynomials.
Please follow the links above to read more about me, my research, teaching, and other things I get up to
Numerical simulation of defocusing NLS. The initial profile resolves into a train of solitons plus a decaying radiation term
Emergence of a dispersive shock wave (DSW) under the Korteweg-de Vries evolution. The gradient catasrophe is regularized by dispersing the energy into a slowly modulated envelope of rapid oscillations.
The rescaled complex zeros (blue dots) of the Taylor polynomials of cosh(z) of degree n, for n from 10 to 200. The zeros converge to the Szego fixed curve, a first correction which gives a better approximation for finite n is also shown. The zeros on the imaginary interval inside the Szego curve converge exponentially fast to the true zeros of cosh(z).