Research:

Research interests: Partial differential equations, harmonic analysis.

I work on nonlinear dispersive and wave equations, especially equations that originate in physics.

Papers:

• The gauge-invariant I-method for Yang-Mills. (2022) (57 pages)

• (with Benjamin Dodson) Instability of the soliton for the focusing, mass-critical generalized KdV equation. Discrete and Continuous Dynamical Systems, Vol. 42, Number 4, 2022

• (with Casey Jao and Daniel Tataru) Wave maps on (1+2)-dimensional curved spacetimes. (100 pages) Analysis & PDE, Vol. 14 (2021), No. 4, 985-1084

• A deterministic counterexample for high dimensional L2L∞ Strichartz estimates for the wave equation. To appear in Proceedings of the Conference on Geometric and Functional Inequalities and Recent Topics in Nonlinear PDEs, AMS 2021

• Global well-posedness for the energy critical massive Maxwell-Klein-Gordon equation with small data (101 pages)

Annals of PDE, vol. 5, Article number: 10 (2019)

• Global well-posedness of high dimensional Maxwell-Dirac for small critical data. (79 pages) Memoirs of the AMS, 2020; Vol. 264, Number 1279

• PhD Thesis, UC Berkeley: Global well-posedness and parametrices for critical Maxwell-Dirac and massive Maxwell-Klein-Gordon equations with small Sobolev data

• Master's degree thesis: Dispersion property for the discrete Schrodinger equations on networks at SNSB Bucharest - research project with Liviu Ignat

Selected talks:

• The gauge-invariant I-method for Yang-Mills. Oct. 2022, Bielefeld

• Instability of the soliton for the focusing, mass-critical generalized KdV equation. Feb. 2021 (Online conference)

• Wave maps on (1+2)-dimensional curved spacetimes. Nov. 2018, Purdue University

Teaching:

At Johns Hopkins:

Math 631: Partial Differential Equations I (Graduate course)

Math 443: Fourier Analysis

Math 311: Methods of Complex Analysis

Math 107: Calculus II (Biological and Social Sciences)

Math 406: Real Analysis II

Math 407: Honors Complex Analysis

Math 405: Introduction to Real Analysis

Pioneer Academics: Course on Fourier analysis