
Prof. Dr. Christian Brennecke
Institute for Applied MathematicsUniversity of Bonn
Endenicher Allee 60
53115 Bonn, Germany
Office:
Phone: Email: |
2.060 +49 228 73 2446 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
- (with J. Lee, P. T. Nam) Second Order Expansion of Gibbs State Reduced Densities in the Gross-Pitaevskii Regime. arXiv
- (with C. Xu, H.-T. Yau) Operator Norm Bounds on the Correlation Matrix of the SK Model at High Temperature. arXiv
- (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
- (with A. Adhikari, C. Xu, H.-T. Yau) Spectral Gap Estimates for Mixed p-Spin Models at High Temperature. arXiv
- Bogoliubov Theory for Ultra Dilute Bose Gases. To appear in the proceedings of IQM22, Politecnico di Milano (2023)
- The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime. J. Math. Phys. 63, 051101 (2022). arXiv - Article
- (with H.-T. Yau) The Replica Symmetric Formula for the SK Model Revisited. J. Math. Phys. 63, 073302 (2022). arXiv - Article
- (with B. Schlein, S. Schraven) Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime. Ann. Henri Poincaré 23 1583–1658 (2022). arXiv - Article
- (with M. Caporaletti, B. Schlein) Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime. Rev. Math. Phys. 34 , no. 09 (2022). arXiv - Article
- (with P. von Soosten) On the mean-field equations for ferromagnetic spin systems. Lett. Math. Phys. 111, 108 (2021). arXiv - Article
- (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
- (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 (2021). 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 , 1311-1395 (2020). arXiv - Article
- (with C. Boccato, S. Cenatiempo, B. Schlein) Bogoliubov Theory in the Gross-Pitaevskii Limit. Acta Mathematica 222 , no. 2, 219-335 (2019). 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 , no. 5, 1201-1235 (2019). arXiv - Article
- (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
- (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
- (with B. Schlein) Gross-Pitaevskii Dynamics for Bose-Einstein Condensates. Analysis & PDE 12 , no. 6, 1513-1596 (2019). arXiv - Article
- (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