Christian Brennecke

Christian Brennecke

Harvard University
Department of Mathematics
1 Oxford Street
Cambridge, MA 02138, USA

Office:
Email:
Science Center 239
brennecke Christian Brennecke math.harvard.edu


About me

Starting in the fall 2021, I will work as a Bonn Junior Fellow at the University of Bonn. Previously, I was employed as a Benjamin Peirce Fellow at Harvard University, where I have been working with Horng-Tzer Yau. I received my Ph.D. in 2018 from the University of Zurich, where my advisor was Benjamin Schlein. Here is my CV.

Research interests

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

  1. (with M. Caporaletti, B. Schlein) Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime.   arXiv
  2. (with P. von Soosten) On the mean-field equations for ferromagnetic spin systems.   arXiv
  3. (with B. Schlein, S. Schraven) Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime.   arXiv
  4. (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
  5. (with A. Adhikari, B. Schlein) Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime. Ann. Henri Poincaré 22, 1163-1233.   arXiv - Article
  6. (with A. Adhikari) Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field. J. Math. Phys. 61 , 083302 (2020).   arXiv - Article
  7. (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
  8. (with C. Boccato, S. Cenatiempo, B. Schlein) Bogoliubov Theory in the Gross-Pitaevskii Limit. Acta Mathematica 222 (2019), no. 2, 219-335.   arXiv - Article
  9. (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
  10. (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
  11. (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
  12. (with B. Schlein) Gross-Pitaevskii Dynamics for Bose-Einstein Condensates. Analysis & PDE 12 (2019), no. 6, 1513-1596.   arXiv - Article
  13. (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