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; 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 \(L^2(\mathbb{R})\).
*Submitted*, 2022.
- (with G. Dubach and P. Germain) On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model.
*Submitted*, 2022.
- (with R. Killip and M. Vişan) Sharp well-posedness for the cubic NLS and mKdV in \(H^s(\mathbb{R})\).
*Submitted*, 2020.
- (with J. Bedrossian and P. Germain) Vortex filament solutions of the Navier-Stokes equations.
*Comm. Pure Appl. Math.*, to appear.
- (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, M. Ntekoume, and M. Vişan) Global well-posedness for the derivative nonlinear Schrödinger equation in \(L^2(\mathbb{R})\).
*Submitted*, 2022.
- (with G. Dubach and P. Germain) On the derivation of the homogeneous kinetic wave equation for a nonlinear random matrix model.
*Submitted*, 2022.
- (with R. Killip and M. Vişan) Large-data equicontinuity for the derivative NLS.
*Int. Math. Res. Not. IMRN*, to appear.
- (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 \(H^s(\mathbb{R})\).
*Submitted*, 2020.
- (with J. Bedrossian and P. Germain) Vortex filament solutions of the Navier-Stokes equations.
*Comm. Pure Appl. Math.*, to appear.
- (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 2022 semester I am teaching:

- MATH-673: Complex Variables.

Class details may be found on Canvas.

## Previous teaching

### Instructor, Georgetown University

### 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.

## About

I live in Washington DC with my wife, daughter, 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.