To date, my work is broadly in the area of nonlinear partial differential equations. During my master's and the first part of my PhD, my work was in problems dealing with asymptotic behavior for nonlinear Schrodinger equations.
My current work deals with paracontrolled calculus and its application to singular stochastic partial differential equations, specifically to SPDE models coming from continuum limits of lattice dynamics and from geometric heat flows.
Preprints and Publications
Higher-Order Paracontrolled Calculus for Geometric Rough Paths, submitted (2026)
A Global Wavefront Set Condition for Defining Bony's Paraproduct Decomposition,
joint with Josh Mott, submitted (2026)
On Analyticity of Solitons for the Periodic Dispersion-Managed Nonlinear Schrödinger Equation , joint with Sebastian Herr, Dirk Hundertmark and Jeremy L. Marzuola, submitted (2026)
Modified Scattering for Nonlocal Nonlinear Schrödinger Equations, submitted. (2025)
Modified Scattering for the Hartree Nonlinear Schrödinger Equation, (2024).
Modified Scattering for the Schrödinger-Bopp-Podolsky Equation, (2023).
Averaging for the Dispersion-Managed Nonlinear Schrödinger Equation, joint with Luccas Campos and Jason Murphy, Commun. Contemp. Math. 26, no. 7, Article no. 2350030 (2024).
Well-Posedness and Blowup for the Dispersion-Managed Nonlinear Schrödinger Equation, joint with Jason Murphy, Proc. Amer. Math. Soc. 151 (2023), no. 6, 2489–2502.
Modified Scattering for a Dispersion-Managed Nonlinear Schrödinger Equation, joint with Jason Murphy, NoDEA Nonlinear Differential Equations Appl. 29 (2022), no. 1, Art. 1, 11pp.