I am an Assistant Professor in the Department of Mathematics and Statistics at Georgetown University.
Research
My research interests are in PDE and analysis. Primarily, I work on problems arising from the study of nonlinear waves and fluid dynamics. My current interests include: integrable PDEs; vortex filaments; wave turbulence; Gaussian processes; degenerate dispersive equations and compactons; surface and internal waves.
Selected publications
- (with R. Killip, M. Ntekoume, and M. Vişan) Global well-posedness for the derivative nonlinear Schrödinger equation in \(L^2(\mathbb{R})\). J. Eur. Math. Soc. (JEMS), to appear.
- (with G. Dubach and P. Germain) On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model. Ars Inven. Anal., 2023:Paper No. 7, 2023.
- (with R. Killip and M. Vişan) Sharp well-posedness for the cubic NLS and mKdV in \(H^s(\mathbb{R})\). Forum Math. Pi, 12:Paper No. e6, 2024.
- (with J. Bedrossian and P. Germain) Vortex filament solutions of the Navier-Stokes equations. Comm. Pure Appl. Math., 76(4):685–787, 2023.
- (with P. Germain and J. L. Marzuola) Existence and uniqueness of solutions for a quasilinear KdV equation with degenerate dispersion. Comm. Pure Appl. Math., 72(11):2449–2484, 2019.
- (with M. Ifrim and D. Tataru) Finite depth gravity water waves in holomorphic coordinates. Ann. PDE, 3(1):Paper No. 4, 2017.
Full publication list
- (with R. Killip and M. Vişan) The nonlinear Schrödinger equation with sprinkled nonlinearity. Submitted, 2024.
- (with R. Killip, M. Ntekoume, and M. Vişan) Global well-posedness for the derivative nonlinear Schrödinger equation in \(L^2(\mathbb{R})\). J. Eur. Math. Soc. (JEMS), to appear.
- (with G. Dubach and P. Germain) On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model. Ars Inven. Anal., 2023:Paper No. 7, 2023.
- (with R. Killip and M. Vişan) Large-data equicontinuity for the derivative NLS. Int. Math. Res. Not. IMRN, 2023(6):4601–4642, 2023.
- (with R. Killip and M. Vişan) Microscopic conservation laws for integrable lattice models. Monatsh. Math., 196(3):477–504, 2021.
- (with J. L. Marzuola) Local well-posedness for a quasilinear Schrödinger equation with degenerate dispersion. Indiana Univ. Math. J., 71(4):1585–1626, 2022.
- (with R. Killip and M. Vişan) Sharp well-posedness for the cubic NLS and mKdV in \(H^s(\mathbb{R})\). Forum Math. Pi, 12:Paper No. e6, 2024.
- (with J. Bedrossian and P. Germain) Vortex filament solutions of the Navier-Stokes equations. Comm. Pure Appl. Math., 76(4):685–787, 2023.
- (with P. Germain and J. L. Marzuola) Existence and uniqueness of solutions for a quasilinear KdV equation with degenerate dispersion. Comm. Pure Appl. Math., 72(11):2449–2484, 2019.
- (with P. Germain and J. L. Marzuola) Compactons and their variational properties for degenerate KdV and NLS in dimension 1. Quart. Appl. Math., 78(1):1–32, 2020.
- (with J. L. Marzuola) Small data global solutions for the Camassa-Choi equations. Nonlinearity, 31(5):1868–1904, 2018.
- (with M. Ifrim and D. Tataru) Finite depth gravity water waves in holomorphic coordinates. Ann. PDE, 3(1):Paper No. 4, 2017.
- (with M. Ifrim and D. Tataru) The lifespan of small data solutions to the KP-I. Int. Math. Res. Not. IMRN, 2017(1):1–28, 2017.
- Long time behavior of solutions to the mKdV. Comm. Partial Differential Equations, 41(2):282–317, 2016.
- Large data local well-posedness for a class of KdV-type equations II. Int. Math. Res. Not. IMRN, 2015(18):8590–8619, 2015.
- Large data local well-posedness for a class of KdV-type equations. Trans. Amer. Math. Soc., 367(2):755–773, 2015.
Teaching
During the Fall 2024 semester I am teaching:
- MATH-3300: Differential Geometry
- MATH-8100: Real Analysis
Class details may be found on Canvas.
Previous teaching
Instructor, Georgetown University
- MATH-8130: Complex Variables, Spring 2024.
- MATH-4320: Complex Analysis, Fall 2023.
- MATH-8100: Real Analysis, Fall 2023.
- MATH-673: Complex Variables, Fall 2022.
Instructor, UCLA
- Math 32B: Calculus of Several Variables, Spring 2022.
- Math 134: Linear and Nonlinear Systems of Differential Equations, Winter 2022.
- Math 170E: Introduction to Probability and Statistics: Probability, Winter 2022.
- Math 32B: Calculus of Several Variables, Fall 2021.
- Math 134: Linear and Nonlinear Systems of Differential Equations, Fall 2021.
- Graduate Bootcamp, Summer 2021.
- Math 131C: Topics in Analysis, Spring 2021.
- Math 32B: Calculus of Several Variables, Winter 2021.
- Math 135: Ordinary Differential Equations, Winter 2021.
- Math 134: Linear and Nonlinear Systems of Differential Equations, Fall 2020.
- Math 170E: Introduction to Probability and Statistics: Probability, Spring 2020.
- Math 170E: Introduction to Probability and Statistics: Probability, Winter 2020.
- Math 170B: Probability Theory, Fall 2019.
- Math 131B: Analysis, Spring 2019.
- Math 32B: Calculus of Several Variables, Winter 2018.
- Math 32B: Calculus of Several Variables, Fall 2018.
Instructor, New York University
- MATH-UA 120: Discrete Mathematics, Spring 2018.
- MATH-UA 262: Ordinary Differential Equations, Fall 2017.
- MATH-UA 121: Calculus 1, Fall 2016.
TA, University of California, Berkeley
- Math 16A: Analytic Geometry and Calculus, Fall 2014.
- Math 53: Multivariable Calculus, Fall 2013.
- Math 202B: Introduction to Topology & Analysis, Spring 2013.
- Math 16B: Analytic Geometry and Calculus, Spring 2012.
- Math 54: Linear Algebra & Differential Equations, Fall 2011.
- Math 53: Multivariable Calculus, Spring 2011.
- Math 1A: Calculus, Fall 2010.
Funding
My work is generously supported by:
Previous funding
About
I live in Washington DC with my wife, daughter, son, and greyhound. I grew up in London, UK and have been in DC since 2022. I was previously an Assistant Adjunct Professor at the University of California, Los Angeles and a Simons Junior Fellow at the Courant Institute, NYU. I completed my PhD at the University of California, Berkeley, where my advisor was Daniel Tataru, and my undergraduate degree at Magdalen College, Oxford.
