About Me

My formal CV as of July 2021 can be found here.

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 2009-2010, I was at Columbia University as a National
Science Foundation Postdoctoral Research Fellow working with Professor
Michael Weinstein.  However, I spent the academic year 2008-2009 as a Hausdorff Center
Postdoc with Professor Herbert Koch at the University of Bonn.

Presently, I am a Professor in the Analysis Group at the University of North Carolina at Chapel Hill, where I am lucky enough to study/discuss PDE using tools from microlocal analysis almost every day with my PDE colleagues Arunima Bhattacharya, Yaiza Canzani, Hans Christianson, Jason Metcalfe, Casey Rodriguez, Michael Taylor, and Mark Williams. In addition, I get to talk about models, applications and numerics with Chris Jones, Katie Newhall, Boyce Griffith, Jingfang Huang, Shahar Kovalsky as well as members of our Applied Fluids Group such as Roberto Camassa and Rich McLaughlin.  I have also started working with several members from Statistics, such as Nico Fraiman, Amarjit Budhiraja and Sayan Banerjee.

My research interests include soliton and vortex existence/stability, well-posedness theory for quasilinear and degenerate models, linear scattering theory, spectral theory, Strichartz/dispersive estimates, microlocal analysis, properties of eigenfunctions on billiards, classical dynamics descriptions of PDE solutions, graph Laplacian spectral problems, quantum graphs, numerical simulations, asymptotic analysis, degenerate dispersive/diffusive equations with applications in nonlinear optics, fluid dynamics, topological physics, material science, quantum mechanics, general relativity, quantum chemistry, statistical physics, weak turbulence.

Research supported in part by NSF Applied Math Grant DMS-1312874 (2013-2017), NSF CAREER Grant DMS-1352353 (2014-2020), NSF Applied Math Grant DMS-1909035 (2019-2023) and NSF Applied Math Grant DMS-2307384 (2023-present).  I am also a Co-PI on a new NSF RTG grant DMS-2135998 for the PDE group (PI Jason Metcalfe, Co-PIs Yaiza Canzani, Hans Christianson) and a Co-PI on a new NSF FRG grant DMS-2152289 joint between UNC and UIC (PI Kai Zhang, Co-PIs Jingfang Huang, Yao Li, Shahar Kovalsky, Yichao Wu, Ping-Shou Zhong).