I am interested in the analysis of partial differential equations, especially nonlinear dispersive equations and their applications in mathematical fluid dynamics. My research topics so far include low regulartity well-posedness of dispersive PDEs, existence of solitary waves in two-dimensional water waves & approximations.
On the gravity-capillary water waves with point vortices (2025) 55 pages
https://arxiv.org/abs/2504.17951
Low regularity well-posedness for two-dimensional deep water waves (2024) 59 pages
https://arxiv.org/abs/2410.05201
On the capillary water waves with constant vorticity (2025)
https://arxiv.org/abs/2410.11762 Journal of Differential Equations.
Two-dimensional solitary water waves with constant vorticity, Part II: the deep capillary case (2024) 29 pages
With James Rowan. https://arxiv.org/abs/2408.03428
Low regularity well-posedness for two dimensional deep gravity water waves with constant vorticity (2025)
https://arxiv.org/abs/2312.09347 Communications in Partial Differential Equations.
Two dimensional solitary water waves with constant vorticity, Part I: the deep gravity case (2023) 28 pages
With James Rowan. https://arxiv.org/abs/2305.04483
The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity (2022)
With Mihaela Ifrim, James Rowan and Daniel Tataru. Ars Inveniendi Analytica.
Two dimensional gravity-capillary water waves at low regularity.
PDE Seminar at Vanderbilt University Nov 8 2024
Low regularity well-posedness of 2D capillary water waves.
PDE-Applied Math Seminar at University of Maryland Oct 17 2024 University
On the capillary water waves with constant vorticity.
Nonlinear PDEs Summer School at UC Berkeley Jun 14 2024
Low regularity well-posedness for deep gravity water waves with constant vorticity.
2024 Spring AMS Central Sectional Meeting at UWM Apr 21 2024
Two dimensional gravity water waves with constant vorticity at low regularity.
Harmonic Analysis & Differential Equations Seminar at University of California, Berkeley Apr 16 2024
Gravity water waves with constant vorticity at low regularity and balanced energy estimates.
M. E. Taylor Analysis & PDE Seminar at University of North Carolina at Chapel Hill Apr 10 2024
Two dimensional deep capillary solitary water waves with constant vorticity.
Graduate Analysis and PDEs Seminar at UW-Madison Apr 1 2024
Existence of deep capillary solitary water waves with constant vorticity.
Spring School on Soliton Dynamics at Texas A&M University Mar 16 2024
On the well-posedness and decay estimate of third order Benjamin-Ono equation.
Specialty exam at UW-Madison Nov 16 2022
The Benjamin-Ono approximation for 2D gravity water waves with constant vorticity.
PDE & Geometric Analysis Seminar at UW-Madison Nov 1 2021
The L^2 well-posedness of Benjamin-Ono equation.
Mathematical Problems in Fluid Dynamics Graduate Student Seminar at MSRI (virtual) Apr 7 2021
Nonlinear PDEs Summer School at UC Berkeley, California, June 2024.
2024 Spring AMS Central Sectional Meeting: Special Session on Nonlinear waves, Milwaukee, Wisconsin, April 2024.
Spring School on Soliton Dynamics, College Station, Texas, March 2024
SLMath program Mathematical Problems in Fluid Dynamics II, Berkeley, California, July and August 2023.
Oberwolfach Seminar: Free Boundary Problems in Fluid Dynamics, Oberwolfach, Germany, October 2022.
Summer School 2022: Geometric dispersive PDEs, Obergurgl, Austria, September 2022.
Harmonic Analysis and Waves, Seattle, Washington, August 2022.
Michigan Research Experience for Graduates 2022, June 2022.
PDE virtual research seminar on Water Waves, September 2020 - May 2021.
MSRI program Mathematical problems in fluid dynamics during Spring 2021.
Graduate summer school at MSRI: Introduction to Water Waves, August 2020.