L.E. Dickson Instructor
University of Chicago
I am an Assistant Professor at the University of Chicago.
Department of Mathematics
University of Chicago
5734 S. University Ave
Chicago, Illinois 60637
Here is my cv.
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.
PhD in Mathematics 2010-2015, MIT. Advisor: Gigliola Staffilani.
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
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
(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
(with B. Dodson and J. Lührmann). Adv. Math. 347 (2019), 619–676.
Almost sure boundedness of iterates for derivative nonlinear wave
(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
(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
(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
(with J. Lührmann). New York J. Math, 22 (2016) 209-227.
non-squeezing for the cubic nonlinear Klein-Gordon equation on
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
(with A. Nachmias and S. S. Watson). Comm. Math. Phys., 329 (2014), no. 1, 29-56.