My research area is mathematical physics. More specifically, I am interested in the analysis of many-body systems from quantum mechanics and statistical physics, such as Bose-Einstein condensates and spin glasses.
Teaching
In the fall 2021, I will be teaching a topics course on many-body quantum mechanics. A course syllabus can be found here.
Publications & Preprints
(with M. Caporaletti, B. Schlein)
Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime. arXiv
(with P. von Soosten)
On the mean-field equations for ferromagnetic spin systems. arXiv
(with B. Schlein, S. Schraven)
Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime. arXiv
(with A. Adhikari, P. von Soosten, H.-T. Yau)
Dynamical Approach to the TAP Equations for the Sherrington-Kirkpatrick Model. J. Stat. Phys. 183, 35 (2021) . arXiv - Article
(with A. Adhikari, B. Schlein)
Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime. Ann. Henri Poincaré 22, 1163-1233. arXiv - Article
(with A. Adhikari)
Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field. J. Math. Phys. 61 , 083302 (2020).
arXiv - Article
(with C. Boccato, S. Cenatiempo, B. Schlein)
Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime. Comm. Math. Phys. 376 (2020), 1311-1395.
arXiv - Article
(with C. Boccato, S. Cenatiempo, B. Schlein)
Bogoliubov Theory in the Gross-Pitaevskii Limit. Acta Mathematica 222 (2019), no. 2, 219-335.
arXiv - Article
(with P.T. Nam, M. Napiórkowski, B. Schlein)
Fluctuations of N-particle quantum dynamics around the nonlinear Schrödinger equation. Ann. Inst. Henri Poincaré C - Anal. Non Linéaire 36 (2019), no. 5, 1201-1235.
arXiv - Article
(with C. Boccato, S. Cenatiempo, B. Schlein)
The excitation spectrum of Bose gases interacting through singular potentials. J. Eur. Math. Soc. 22 (2020), 2331-2403.
arXiv - Article
(with C. Boccato, S. Cenatiempo, B. Schlein)
Complete Bose-Einstein condensation in the Gross-Pitaevskii regime. Comm. Math. Phys. 359 (2018), no. 3, 975-1026.
arXiv - Article
(with B. Schlein)
Gross-Pitaevskii Dynamics for Bose-Einstein Condensates. Analysis & PDE 12 (2019), no. 6, 1513-1596.
arXiv - Article
(with A. Linke, C. Merdon, J. Schoberl)
Optimal and pressure-independent L2 velocity error estimates for a modied Crouzeix-Raviart Stokes element with BDM reconstructions. Journal of Computational Mathematics 33 (2015), no. 2, 191-208.
Article