Prof. Dr. Christian Brennecke

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

Office: Phone: Email:

2.060 +49 228 73 2446 brennecke iam.uni-bonn.de

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