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 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. Here is my CV.Research Interests
My research area lies at the intersection of analysis, mathematical physics and probability theory. More specifically, I am interested in the study of interacting 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 W. Kroschinsky) Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators arXiv
- (with A. Schertzer, C. Van Dam) Spin Covariance Fluctuations in the SK Model at High Temperature. arXiv
- (with M. Brooks, C. Caraci, J. Oldenburg) A Short Proof of Bose- Einstein Condensation in the Gross-Pitaevskii Regime and Beyond. Ann. Henri Poincaré (2024). arXiv
- (with J. Lee, P. T. Nam) Second Order Expansion of Gibbs State Reduced Densities in the Gross-Pitaevskii Regime. SIAM Journal on Mathematical Analysis. 56, Iss. 4 (2024) 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. Prob. Math. Phys. 5, No. 1, 131–175 (2024). arXiv - article
- (with A. Adhikari, C. Xu, H.-T. Yau) Spectral Gap Estimates for Mixed p-Spin Models at High Temperature. Probab. Theory Relat. Fields 189 , 879–907 (2024). arXiv - article
- 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
- The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime. J. Math. Phys. 63 (2022). arXiv - article
- (with H.-T. Yau) The Replica Symmetric Formula for the SK Model Revisited. J. Math. Phys. 63 (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 (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