### About

My research is in the area of nonlinear partial differential equations (PDE). Particulary, I study equations modeling *wave-type phenomena*, which are often called *nonlinear dispersive PDE*. Such equations arize in quantum mechanics, nonlinear optics, plasma physics, oceanography, and all the way to general relativity. Mathematically, the central question is to understand the behavior of solutions to those equations either deterministically (what happens to every solution) or probabilistically (what happens to generic solutions). Part of the beauty of this field comes from the diverse mathematical areas that contribute to its analysis including harmonic analysis, PDE theory, dynamical systems, probability theory, and sometimes even analytic number theory.