I am a Postdoctoral Researcher in the Mathematics Institute at the University of Zurich. My host is Benjamin Schlein. My fields of interest are Nonlinear Dispersive Equations, Harmonic Analysis, and Quantum many-body problems.
Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations, MIT Doctoral Thesis, June 2011.
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.
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 2D Hartree Equations, Discrete and Continuous Dynamical Systems A, Volume 32, Number 10 (2012), 3733-3771.
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.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.
Randomization and the Gross-Pitaevskii hierarchy (with Gigliola Staffilani), Archive for Rational Mechanics and Analysis, Volume 218, Issue 1 (2015), 417–485.
Local existence of solutions to Randomized Gross-Pitaevskii hierarchies, Transactions of the American Mathematical Society, Volume 368, Number 3 (2016), 1759–1835.
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.
The Gross-Pitaevskii hierarchy on general rectangular tori, (with Sebastian Herr), Archive for Rational Mechanics and Analysis, Volume 220, Issue 3 (2016), 1119-1158.
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.
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.
At the University of Zurich:
At ETH Zurich:
At the University of Pennsylvania: