Ph.D. University of Texas at Austin, 2017
I have a wide range of research interests in nonlocal evolution equations. Most of my work is in nonlinear kinetic equations - namely, the Boltzmann and Landau (Fokker-Planck) equations concerning long-range intermolecular interactions, such as in plasmas. I am interested in entropy methods, Cercignani's conjecture and long time behavior for such equations, as well as well posed-ness, regularity and integrability. Additionally, I am involved in nonlocal hyperbolic conservation laws. In particular I work on the formation, propagation and stability of (fractional) shock waves. I am interested in fractional diffusion, nonlinear waves and hydrodynamic limits.
(Differential Calculus), Fall 2010, Spring 2011, Summer 2014.
(Integral Calculus), Spring 2012, Summer 2013.
(Differential Calculus for Natural Sciences), Fall 2012.
(Ordinary Differential Equations), Fall 2013.
(Methods of Applied Mathematics - a graduate course in functional analysis and PDE), Spring 2014.