Teaching Responsibilities 2021/22:
Term 2: MA4A7 Quantum Mechanics
Research Interests: Nonlinear dispersive PDEs, Many-body quantum problems.
(19) A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation (with Andrew Rout), Preprint (2022), 42 pages, arXiv: 2206.03392.
(18) The Euclidean $\phi^4_2$ theory as a limit of an interacting Bose gas (with Jürg Fröhlich, Antti Knowles, and Benjamin Schlein), Preprint (2022), 53 pages, arXiv: 2201.07632.
(17) Gibbs measures as unique KMS equilibrium states of Hamiltonian PDEs (with Zied Ammari), Preprint (2021), 52 pages, arXiv: 2102.12202. To appear in Revista Matemática Iberoamericana.
(16) Interacting loop ensembles and Bose gases (with Jürg Fröhlich, Antti Knowles, and Benjamin Schlein), Preprint (2020), 55 pages, arXiv: 2012.05110.
(15) A path-integral analysis of interacting Bose gases and loop gases (with Jürg Fröhlich, Antti Knowles, and Benjamin Schlein), Journal of Statistical Physics 180. (2020), no.1-6, 810-831.
(14) The mean-field limit of quantum Bose gases at positive temperature (with Jürg Fröhlich, Antti Knowles, and Benjamin Schlein), Preprint (2020), 74 pages, arXiv: 2001.01546. To appear in the Journal of the American Mathematical Society.
(13) A microscopic derivation of Gibbs measures for nonlinear Schrödinger equations with unbounded interaction potentials, Preprint (2019), 78 pages, arXiv: 1904.08137. To appear in International Mathematics Research Notices, doi: 10.1093/imrn/rnab132.
(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).
University of Warsaw, Physics Seminar, December 9, 2021.
Texas A&M University, Nonlinear Partial Differential Equations Seminar, November 30, 2021.
Winter School: Turbulence in fluids and PDEs, EPFL, Lausanne, January 27–31, 2020.
Quantissima in the Serenissima III, Venice, Italy, August 19–23, 2019.
University of Oxford, Stochastic Analysis Seminar, June 10, 2019.
Recent research grants:
EPSRC New Investigator Award, September 2020-present.
Simons Postdoctoral Fellowship, University of Pennsylvania: July 2011-June 2014.
Recent awards & prizes:
Warwick Award for Personal Tutoring Excellence nomination: 2022.
Warwick Award for Teaching Excellence nomination: 2019, 2020.
ERC Starting Grant Finalist: June 2018.
Good Teaching Prize, University of Pennsylvania: Fall 2011 and Spring 2013.
Charles and Jennifer Johnson Prize for an accepted publication, MIT: Spring 2011.