Christian Brennecke Christian Brennecke

Prof. Dr. Christian Brennecke

Institute for Applied Mathematics
University of Bonn
Endenicher Allee 60
53115 Bonn, Germany

+49 228 73 2446
brennecke Christian Brennecke

About Me

Since October 2021, I am a professor (Bonn Junior Fellow) at the Institute for Applied Mathematics at the University of Bonn. Before coming to Bonn, I was a Benjamin Peirce Fellow at Harvard University. 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 mechanics, with a current focus on Bose-Einstein condensates and mean field spin glasses.

Publications & Preprints

  1. (with M. Brooks, C. Caraci, J. Oldenburg) A Short Proof of Bose- Einstein Condensation in the Gross-Pitaevskii Regime and Beyond.   arXiv
  2. (with J. Lee, P. T. Nam) Second Order Expansion of Gibbs State Reduced Densities in the Gross-Pitaevskii Regime. To appear in SIAM Journal for Mathematical Analysis.   arXiv
  3. (with C. Xu, H.-T. Yau) Operator Norm Bounds on the Correlation Matrix of the SK Model at High Temperature.   arXiv
  4. (with A. Schertzer, C. Xu, H.-T. Yau) The Two Point Function of the SK Model without External Field at High Temperature. Prob. Math. Phys. 5, No. 1 (2024).   arXiv - article
  5. (with A. Adhikari, C. Xu, H.-T. Yau) Spectral Gap Estimates for Mixed p-Spin Models at High Temperature. Probab. Theory Relat. Fields (2024).   arXiv - article
  6. Bogoliubov Theory for Ultra Dilute Bose Gases. In: M. Correggi, M. Falconi (eds), Quantum Mathematics II. INdAM 2022, Springer INdAM Series 58, Springer, Singapore (2023).   article
  7. The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime. J. Math. Phys. 63, 051101 (2022).   arXiv - article
  8. (with H.-T. Yau) The Replica Symmetric Formula for the SK Model Revisited. J. Math. Phys. 63, 073302 (2022).   arXiv - article
  9. (with B. Schlein, S. Schraven) Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime. Ann. Henri Poincaré 23 1583–1658 (2022).   arXiv - article
  10. (with M. Caporaletti, B. Schlein) Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime. Rev. Math. Phys. 34 , no. 09 (2022).   arXiv - article
  11. (with P. von Soosten) On the mean-field equations for ferromagnetic spin systems. Lett. Math. Phys. 111, 108 (2021).   arXiv - article
  12. (with B. Schlein, S. Schraven) Bose-Einstein Condensation with Optimal Rate for Trapped Bosons in the Gross-Pitaevskii Regime. Math. Phys. Anal. Geom. 25, 12 (2022).   arXiv - article
  13. (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
  14. (with A. Adhikari, B. Schlein) Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime. Ann. Henri Poincaré 22, 1163-1233 (2021).   arXiv - article
  15. (with A. Adhikari) Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field. J. Math. Phys. 61 , 083302 (2020).   arXiv - article
  16. (with C. Boccato, S. Cenatiempo, B. Schlein) Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime. Comm. Math. Phys. 376 , 1311-1395 (2020).   arXiv - article
  17. (with C. Boccato, S. Cenatiempo, B. Schlein) Bogoliubov Theory in the Gross-Pitaevskii Limit. Acta Mathematica 222 , no. 2, 219-335 (2019).   arXiv - article
  18. (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 , no. 5, 1201-1235 (2019).   arXiv - article
  19. (with C. Boccato, S. Cenatiempo, B. Schlein) The excitation spectrum of Bose gases interacting through singular potentials. J. Eur. Math. Soc. 22 , 2331-2403 (2020).   arXiv - article
  20. (with C. Boccato, S. Cenatiempo, B. Schlein) Complete Bose-Einstein condensation in the Gross-Pitaevskii regime. Comm. Math. Phys. 359 , no. 3, 975-1026 (2018).   arXiv - article
  21. (with B. Schlein) Gross-Pitaevskii Dynamics for Bose-Einstein Condensates. Analysis & PDE 12 , no. 6, 1513-1596 (2019).   arXiv - article
  22. (with A. Linke, C. Merdon, J. Schöberl) Optimal and pressure-independent L2 velocity error estimates for a modied Crouzeix-Raviart Stokes element with BDM reconstructions. Journal of Computational Mathematics 33, no. 2, 191-208 (2015).   article


Prof. Dr. Lisa Sauermann has been honored with the von Kaven Award 2023 for her outstanding scientific achievements. (16.11.2023)

Prof. Dr. Angkana Rüland has been awarded a New Horizons in Mathematics Prize 2024 for her contributions to applied analysis:

Prof. Dr. Angkana Rüland has been awarded the Calderon Prize that is awarded every two years by the Inverse Problems International Association: (06.09.2023)

Prof. Dr. Karl-Theodor Sturm has been elected into the Academia Europaea. (28.06.2022)

Florian Schweiger erhielt den Hausdorff-Gedächtnispreis 2021 der Fachgruppe Mathematik für die beste Dissertation. Er fertigte die Dissertation unter der Betreuung von Prof. Stefan Müller an. Unter anderen wurde Vanessa Ryborz mit einem Preis der Bonner Mathematischen Gesellschaft für ihre von Prof. Sergio Conti betreute Bachelorarbeit ausgezeichnet. (18.01.2022)

Prof. Dr. Sergio Albeverio has been elected into the Academia Europaea and the Accademia Nazionale dei Lincei (more; 02.12.2021).


Managing Director: Prof. Dr. Juan J. L. Velázquez
Chief Administrator: Dr. B. Doerffel
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Mailing address

Institute for Applied Mathematics
University of Bonn
Endenicher Allee 60
D-53115 Bonn / Germany