I am an Assistant Adjunct Professor in the mathematics department at UCLA.
I completed my PhD in 2015 at the University of California, Berkeley under the supervision of Daniel Tataru. From 2015–2018, I was a Simons Junior Fellow at the Courant Institute, NYU.
I will be on the job market in the Fall of 2021.
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 surface and internal waves.
Selected publications
Full publication list
- (with R. Killip and M. Vişan) Large-data equicontinuity for the derivative NLS. Submitted, 2021.
- (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., to appear.
- (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
I am honored to have received an award for Continued Excellence in Teaching for 2020–2021 from the UCLA mathematics department.
During the Fall 2021 quarter I am teaching:
- Math 32B: Calculus of Several Variables
- Math 134: Linear and Nonlinear Systems of Differential Equations
Class details may be found on CCLE.
Previous teaching
Instructor, UCLA
- Graduate Bootcamp, Summer 2021.
- Topics in Analysis, Spring 2021.
- Calculus of Several Variables, Winter 2021.
- Ordinary Differential Equations, Winter 2021.
- Linear and Nonlinear Systems of Differential Equations, Fall 2020.
- Introduction to Probability and Statistics: Probability, Spring 2020.
- Introduction to Probability and Statistics: Probability, Winter 2020.
- Probability Theory, Fall 2019.
- Analysis, Spring 2019.
- Calculus of Several Variables, Winter 2018.
- Calculus of Several Variables, Fall 2018.
Instructor, New York University
- Discrete Mathematics, Spring 2018.
- Ordinary Differential Equations, Fall 2017.
- Calculus 1, Fall 2016.
TA, University of California, Berkeley
- Analytic Geometry and Calculus, Fall 2014.
- Multivariable Calculus, Fall 2013.
- Introduction to Topology & Analysis, Spring 2013.
- Analytic Geometry and Calculus, Spring 2012.
- Linear Algebra & Differential Equations, Fall 2011.
- Multivariable Calculus, Spring 2011.
- Calculus, Fall 2010.
About
I live in Venice, Los Angeles with my wife, Reesha, and greyhound, Vivian. I am originally from London, UK and have been in Los Angeles since July 2018. I was previously a postdoctoral researcher at the Courant Institute, NYU and a member of the Simons Society of Fellows. I completed my PhD at the University of California, Berkeley, where my advisor was Daniel Tataru, and my undergraduate degree at Magdalen College, Oxford.
