Teaching Responsibilities 2017/18:
Term 2: MA4J0 Advanced Real Analysis
Research Interests: Nonlinear Dispersive PDEs, Harmonic Analysis, Quantum many-body problems.
A microscopic derivation of time-dependent correlation functions of the 1D cubic nonlinear Schrödinger equation, (with Jürg Fröhlich, Antti Knowles, and Benjamin Schlein), Preprint (2017), arXiv:1703.04465.
Gibbs measures of nonlinear Schrödinger equations as limits of quantum many-body states in dimensions d <= 3, (with Jürg Fröhlich, Antti Knowles, and Benjamin Schlein), Preprint (2016), arXiv:1605.07095. To appear in Communications in Mathematical Physics.
The Gross-Pitaevskii hierarchy on general rectangular tori, (with Sebastian Herr), Archive for Rational Mechanics and Analysis, Volume 220, Issue 3 (2016), 1119-1158.
A rigorous derivation of the defocusing cubic nonlinear Schrödinger equation on T^3 from the dynamics of many-body quantum systems, Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire, Volume 32, Number 6 (2015), 1337–1365.
Local existence of solutions to Randomized Gross-Pitaevskii hierarchies, Transactions of the American Mathematical Society, Volume 368, Number 3 (2016), 1759–1835.
Randomization and the Gross-Pitaevskii hierarchy (with Gigliola Staffilani), Archive for Rational Mechanics and Analysis, Volume 218, Issue 1 (2015), 417–485.
On the uniqueness of solutions to the 3D periodic Gross-Pitaevskii hierarchy (with Philip Gressman and Gigliola Staffilani), Journal of Functional Analysis, Volume 266, Number 7 (2014), 4705–4764.
The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space (with Robert Strain), Advances in Mathematics, Volume 261, Number 20 (2014), 274–332.
Bounds on the growth of high Sobolev norms of solutions to 2D Hartree Equations, Discrete and Continuous Dynamical Systems A, Volume 32, Number 10 (2012), 3733-3771.
Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrödinger Equations on R, Indiana University Mathematics Journal, Volume 60, Number 5 (2011), 1487-1516.
Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrödinger Equations on S^1, Differential and Integral Equations, Volume 24, Numbers 7-8 (2011), 653-718.
Quantissima in the Serenissima II, Venice, August 21-25, 2017.
Frontiers in Analysis and Probability, Strasbourg / Zürich meeting, University of Strasbourg, March 23-24,
University of Warwick, Probability Seminar, October 19, 2016.
The 3rd SwissMAP General Meeting, Engelberg, Switzerland, September 11-14, 2016.
Singularity formation and long-time behavior in dispersive PDEs, University of Bonn, March 14-18, 2016.
University of Bielefeld, Oberseminar Analysis, October 30, 2015.
University of California Berkeley, Analysis Seminar, October 5, 2015.
Recent research grants:
Simons Postdoctoral Fellowship, University of Pennsylvania: July 2011-June 2014.
Recent awards & prizes:
Good Teaching Prize, University of Pennsylvania: Fall 2011 and Spring 2013.
Charles and Jennifer Johnson Prize, MIT: Spring 2011.