Teaching Responsibilities 2019/20:
Term 1: MA137 Mathematical Ananlysis
Term 2: MA4J0 Advanced Real Analysis
Research Interests: Nonlinear Dispersive PDEs, Harmonic Analysis, Many-body quantum problems.
My CV .
(13) A microscopic derivation of Gibbs measures for nonlinear Schrödinger equations with unbounded interaction potentials, Preprint (2019), arXiv: 1904.08137.
(12) Unconditional Uniqueness Results for the Nonlinear Schrödinger Equation (with Sebastian Herr), Communications in Contemporary Mathematics, Volume 21, Number 7 (2019), 1850058, 33 pp.
(11) A microscopic derivation of time-dependent correlation functions of the 1D cubic nonlinear Schrödinger equation (with Jürg Fröhlich, Antti Knowles, and Benjamin Schlein), Advances in Mathematics, Volume 353 (2019), 67-115.
(10) 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), Communications in Mathematical Physics, Volume 356, Number 3 (2017), 883--980.
(9) The Gross-Pitaevskii hierarchy on general rectangular tori, (with Sebastian Herr), Archive for Rational Mechanics and Analysis, Volume 220, Issue 3 (2016), 1119-1158.
(8) 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.
(7) Local existence of solutions to Randomized Gross-Pitaevskii hierarchies, Transactions of the American Mathematical Society, Volume 368, Number 3 (2016), 1759–1835.
(6) Randomization and the Gross-Pitaevskii hierarchy (with Gigliola Staffilani), Archive for Rational Mechanics and Analysis, Volume 218, Issue 1 (2015), 417–485.
(5) 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.
(4) 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.
(3) 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.
(2) 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.
(1) 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.
Publications (1)-(3) from the above list were part of my Ph.D. thesis.
Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations, Ph.D. thesis, MIT (2011).
Oberwolfach Mini-Workshop: Gibbs Measures for Nonlinear Dispersive Equations, April 20, 2018.
University of Cambridge, Geometric Analysis and Partial Differential Equations seminar, March 26, 2018.
London Mathematical Society Network on Harmonic Analysis and PDEs, University of Warwick, December 11, 2017.
Quantissima in the Serenissima II, Venice, August 21-25, 2017.
Frontiers in Analysis and Probability, Strasbourg / Zürich meeting, University of Strasbourg, March 23-24,
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.
ERC Starting Grant Finalist: June 2018.
Warwick Award for Teaching Excellence nomination: 2019.