L.E. Dickson Instructor
University of Chicago

{first}@math.uchicago.edu

I am an Assistant Professor at the University of Chicago.

Contact Info

Eckhart 220
Department of Mathematics
University of Chicago
5734 S. University Ave
Chicago, Illinois 60637

CV
Here is my cv.

Research Interests
I am interested in the study of nonlinear dispersive equations, particularly in using probabilistic techniques to study the behaviour of dispersive and Hamiltonian PDEs. My research is supported by the National Science Foundation grant DMS-1800697.

Education
PhD in Mathematics 2010-2015, MIT. Advisor: Gigliola Staffilani.

Previous Employment

L.E. Dickson Instructor, University of Chicago, Fall 2016-Spring 2019
Member of the Institute for Advanced Study, Spring 2016
Viterbi Endowed Postdoctoral Fellow, MSRI, Fall 2015

Research

Construction of L^2 log-log blowup solutions for the mass critical nonlinear Schrödinger equation
(with C. Fan), submitted, 2020.

An eigensystem approach to Anderson localization for multi-particle systems
(with B. Bringmann), To appear in Ann. Henri Poincaré, 2020.

Non-Uniqueness of Bubbling for Wave Maps
(with M. Engelstein), submitted, 2020.

Poisson Commuting Energies for a System of Infinitely Many Bosons
(with Nahmod, Pavlovic, Rosenzweig, Staffilani), submitted, 2019.

A Rigorous derivation of the Hamiltonian structure for the nonlinear Schrödinger equation
(with Nahmod, Pavlovic, Rosenzweig, Staffilani), Adv. Math. 365 (2020).

The focusing energy-critical nonlinear wave equation with random initial data
(with C. Kenig), 2019. To appear in Int. Math. Res. Not.

Scattering for defocusing energy subcritical nonlinear wave equations
(with B. Dodson, A. Lawrie and J. Murphy), 2018. To appear in Analysis & PDE.

Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation
(with B. Dodson and J. Lührmann). Adv. Math. 347 (2019), 619–676.

Almost sure boundedness of iterates for derivative nonlinear wave equations
(with S. Chanillo, M. Czubak, A. Nahmod, G. Staffilani), 2017, to appear in Comm. Anal. Geom.

Almost sure scattering for the 4D energy-critical defocusing NLW equation with radial data
(with B. Dodson and J. Lührmann), 2017. To appear in Amer. J. Math.

An infinite sequence of conserved quantities for the cubic Gross-Pitaevskii hierarchy on R
(with Nahmod, Pavlović, Staffilani). Trans. Amer. Math. Soc 371 (2019), 5179-5202. Available online.

On the almost sure global well-posedness of energy sub-critical nonlinear wave equations on R^3
(with J. Lührmann). New York J. Math, 22 (2016) 209-227.

Symplectic non-squeezing for the cubic nonlinear Klein-Gordon equation on T^3.
J. Funct. Anal. 272 (2017), no. 7, 3019-3092. Available online.

Random data Cauchy theory for nonlinear wave equations of power-type on R^3
(with J. Lührmann). Comm. Partial Differential Equations. 39 (2014), no. 12, 2262-2283.

Rate of convergence for Cardy's Formula
(with A. Nachmias and S. S. Watson). Comm. Math. Phys., 329 (2014), no. 1, 29-56.