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FÜR SCHÜLERiNNEN
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In my Ph.D. thesis I proved upper bounds on the growth of high Sobolev norms of solutions of nonlinear Schrödinger equations using almost conserved quantities. In my subsequent work I considered the Gross-Pitaevskii hierarchy on a periodic domain with the aim of studying uniqueness of solutions to this system. In addition, I have studied the non cut-off Boltzmann equation. More recently, I have worked on the derivation of Gibbs measures of nonlinear Schrödinger equations from many-body dynamics.
 
 
Thesis:
 
 
Bounds on the growth of high Sobolev norms of solutions to nonlinear Schrödinger equations, Ph.D. Thesis, MIT (2011). Advisor: Gigliola Staffilani.
 
 
Papers:
 
 
1) Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrödinger equations on S1, Differential and Integral equations, 34 (2011), no. 7-8, 653–718.
 
 
2) Bounds on the growth of high Sobolev norms of solutions to Nonlinear Schrödinger equations on R, Indiana University Mathematics Journal, 60 (2011), no. 5, 1487–1516.
 
 
3) Bounds on the growth of high Sobolev norms of solutions to 2D Hartree equations, Discrete and Continuous Dynamical Systems A, 32 (2012), no. 10, 3733–3771.
 
 
4) The Boltzmann equation, Besov spaces, and optimal time decay rates in the whole space (with Robert Strain), Advances in Mathematics, 261 (2014), no. 20, 274–332.
 
 
5) On the uniqueness of solutions to the 3D periodic Gross-Pitaevskii hierarchy (with Philip Gressman and Gigliola Staffilani), Journal of Functional Analysis, 266 (2014), no. 7, 4705–4764.
 
 
6) Randomization and the Gross-Pitaevskii hierarchy (with Gigliola Staffilani), Archive for Rational Mechanics and Analysis, 218 (2015), no. 1, 417–485.
 
 
7) Local existence of solutions to Randomized Gross-Pitaevskii hierarchies, Transactions of the American Math- ematical Society, 368 (2016), no. 3, 1759–1835.
 
 
8) A rigorous derivation of the defocusing nonlinear Schrödinger equation on T3 from the dynamics of many-body quantum systems, Annales d l’Institut Henri Poincaré C, Analyse Non-Linéaire, 32 (2015), no. 6, 1337– 1365.
 
 
9) The Gross-Pitaevskii hierarchy on general rectangular tori (with Sebastian Herr), Archive for Rational Mechanics and Analysis, 220 (2016), no. 3, 1119–1158.
 
 
10) Gibbs measures of nonlinear Schrödinger equations as limits of quantum many-body states in dimensions d ≤ 3 (with Jüerg Fröhlich, Antti Knowles, and Benjamin Schlein), preprint (2016), 101 pages. http://arxiv.org/abs/1605.07095.