L.E. Dickson Instructor
University of Chicago

{first}@math.uchicago.edu

I am an L.E. Dickson Instructor at the University of Chicago. My faculty mentor is Carlos Kenig.

Contact Info

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

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.

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

Previous Employment

Member of the Institute for Advanced Study, Spring 2016
Viterbi Endowed Postdoctoral Fellow, MSRI, Fall 2015

Research

Almost sure local well-posedness and scattering for the 4D cubic nonlinear Schrödinger equation (with B. Dodson and J. Lührmann), 2018.

Probabilistic well-posedness for 2D nonlinear wave equations with Q_αβ null forms (with S. Chanillo, M. Czubak, A. Nahmod, G. Staffilani), 2017.

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 A. Nahmod, N. Pavlović, G. Staffilani), 2016.

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 here

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.