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 J. Lee, P. T. Nam) Second Order Expansion of Gibbs State Reduced Densities in the Gross-Pitaevskii Regime.   arXiv
2. (with C. Xu, H.-T. Yau) Operator Norm Bounds on the Correlation Matrix of the SK Model at High Temperature.   arXiv
3. (with A. Schertzer, C. Xu, H.-T. Yau) The Two Point Function of the SK Model without External Field at High Temperature. To appear in Prob. Math. Phys.   arXiv
4. (with A. Adhikari, C. Xu, H.-T. Yau) Spectral Gap Estimates for Mixed p-Spin Models at High Temperature.   arXiv
5. Bogoliubov Theory for Ultra Dilute Bose Gases. To appear in the proceedings of IQM22, Politecnico di Milano (2023)
6. The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime. J. Math. Phys. 63, 051101 (2022).   arXiv - Article
7. (with H.-T. Yau) The Replica Symmetric Formula for the SK Model Revisited. J. Math. Phys. 63, 073302 (2022).   arXiv - Article
8. (with B. Schlein, S. Schraven) Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime. Ann. Henri Poincaré 23 1583–1658 (2022).   arXiv - Article
9. (with M. Caporaletti, B. Schlein) Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime. Rev. Math. Phys. 34 , no. 09 (2022).   arXiv - Article
10. (with P. von Soosten) On the mean-field equations for ferromagnetic spin systems. Lett. Math. Phys. 111, 108 (2021).   arXiv - Article
11. (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
12. (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
13. (with A. Adhikari, B. Schlein) Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime. Ann. Henri Poincaré 22, 1163-1233 (2021).   arXiv - Article
14. (with A. Adhikari) Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field. J. Math. Phys. 61 , 083302 (2020).   arXiv - Article
15. (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
16. (with C. Boccato, S. Cenatiempo, B. Schlein) Bogoliubov Theory in the Gross-Pitaevskii Limit. Acta Mathematica 222 , no. 2, 219-335 (2019).   arXiv - Article
17. (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
18. (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
19. (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
20. (with B. Schlein) Gross-Pitaevskii Dynamics for Bose-Einstein Condensates. Analysis & PDE 12 , no. 6, 1513-1596 (2019).   arXiv - Article
21. (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