I am a Taussky-Todd Postdoctoral Fellow at Caltech.
I am broadly interested in nonlinear partial differential equations. My main areas of research include fluid dynamics, dispersive equations, and wave equations. I have been active in the investigation of long-time behaviour and scattering of solutions to equations from some of these areas.
Previously, during my Ph.D., I was a Visiting Scholar at UC Berkeley. My adviser was Mihai Tohaneanu. My undergraduate studies were done at UC Berkeley, where I worked with Daniel Tataru.
In the spring, I am instructing Math/Applied. Comp. Math (ACM) 142b: PDE and co-developing the Caltech AI Bootcamp.
Papers
A proof of Onsager’s Conjecture for the SQG equation, with P. Isett.
Full polyhomogeneity of the low-energy resolvent for short-range Schrödinger operators, with E. Sussman.
Global asymptotics of nonlinear waves on asymptotically Minkowski spaces (Working title), with J. Wunsch.
Asymptotics for the null condition on asymptotically Minkowski spaces (Working title), with H. Xiong.
What's the Magic Word? A Control Theory of LLM Prompting, with A. Bhargava, C. Witkowski, M. Thomson.
Asymptotics in all regimes for the Schrödinger equation with time-independent coefficients, with E. Sussman.
Pointwise Decay for the Wave Equation on Nonstationary Spacetimes, J. Math. Anal. Appl., (2022), https://doi.org/10.1016/j.jmaa.2022.126939
Global Existence and Pointwise Decay for the Null Condition , with M. Tohaneanu, submitted. [https://arxiv.org/abs/2204.03626]
Optimal Decay for Large-Data Energy-Critical Wave Equations.
Decay Rates for Nonlinear Wave Equations on Asymptotically Flat Spacetimes.
Optimal Decay for Wave Equations on Kerr and Similar Black Hole Backgrounds.
Scattering for Critical Wave Equations with Variable Coefficients, with M. Tohaneanu, Proc. Edin. Math. Soc., 64, 2 (2021), 298--316. [https://arxiv.org/abs/1912.06795]
Teaching
Caltech AI RL Bootcamp (Spring/Summer '24)
Math/Applied and Comp. Math 142b: PDE (Spring '24)
Caltech AI PIML Bootcamp (Spring '24)
Math 108b: Classical Analysis (Winter '24). Lecture notes