Research
Prospective students and postdocs
Current/accepted UCLA students and prospective postdoctoral applicants whose research interests align with mine are welcome to contact me directly. I have mentored undergraduates before, but only undergraduates who are EXTREMELY advanced/well-prepared can be considered due to the relative inaccessibility of my mathematical research.
Fluid mechanics and PDE
I work on the mathematical analysis of PDEs pertaining mainly to incompressible fluid mechanics. The questions I focus on are generally organized in two directions: stability at high Reynolds number and questions related to turbulence (usually with random/stochastic driving and/or initial data in this case).
Kinetic theory and plasma dynamics
I am interested in a variety of questions involving kinetic theory/non-equilibrium statistical mechanics for plasmas and gas dynamics. I have done a lot of work on phase mixing/Landau damping related effects in collisionless or weakly collisional problems, but am also interested in shocks, implosion singularities, and other questions in kinetic theory.
Random dynamical systems
Interested in understanding the dynamical properties of stochastically forced PDEs and ODEs. Interested in questions such as boundedness of partially damped systems, hypoelliptic regularization, quantitative understanding in limiting parameter regimes, such as quantitative lower bounds on Lyapunov exponents and the spectral gap of Markov semigroups, and related questions motivated by turbulence and high dimensional dynamics.