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 and Preprints

1. (with N. Behrmann, S. Rademacher) Exponential Control of Excitations for Trapped BEC in the Gross-Pitaevskii Regime.   arXiv
2. (with A. Schertzer) On the Replica Symmetry of a Variant of the Sherrington-Kirkpatrick Spin Glass.   arXiv
3. (with W. Kroschinsky) Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators.   arXiv
4. (with A. Schertzer, C. Van Dam) Spin Covariance Fluctuations in the SK Model at High Temperature. Electron. Commun. Probab. 30, paper no. 9 (2025).   arXiv - article
5. (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 - article
6. (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 - article
7. (with C. Xu, H.-T. Yau) Operator Norm Bounds on the Correlation Matrix of the SK Model at High Temperature.   arXiv
8. (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
9. (with A. Adhikari, C. Xu, H.-T. Yau) Spectral Gap Estimates for Mixed p-Spin Models at High Temperature. Probab. Theory Relat. Fields 189 (2024).   arXiv - article
10. 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
11. The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime. J. Math. Phys. 63 (2022).   arXiv - article
12. (with H.-T. Yau) The Replica Symmetric Formula for the SK Model Revisited. J. Math. Phys. 63 (2022).   arXiv - article
13. (with B. Schlein, S. Schraven) Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime. Ann. Henri Poincaré 23 (2022).   arXiv - article
14. (with M. Caporaletti, B. Schlein) Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime. Rev. Math. Phys. 34 , no. 09 (2022).   arXiv - article
15. (with P. von Soosten) On the mean-field equations for ferromagnetic spin systems. Lett. Math. Phys. 111, 108 (2021).   arXiv - article
16. (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
17. (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
18. (with A. Adhikari, B. Schlein) Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime. Ann. Henri Poincaré 22 (2021).   arXiv - article
19. (with A. Adhikari) Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field. J. Math. Phys. 61 (2020).   arXiv - article
20. (with C. Boccato, S. Cenatiempo, B. Schlein) Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime. Comm. Math. Phys. 376 (2020).   arXiv - article
21. (with C. Boccato, S. Cenatiempo, B. Schlein) Bogoliubov Theory in the Gross-Pitaevskii Limit. Acta Mathematica 222 , no. 2 (2019).   arXiv - article
22. (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 (2019).   arXiv - article
23. (with C. Boccato, S. Cenatiempo, B. Schlein) The excitation spectrum of Bose gases interacting through singular potentials. J. Eur. Math. Soc. 22 (2020).   arXiv - article
24. (with C. Boccato, S. Cenatiempo, B. Schlein) Complete Bose-Einstein condensation in the Gross-Pitaevskii regime. Comm. Math. Phys. 359 , no. 3 (2018).   arXiv - article
25. (with B. Schlein) Gross-Pitaevskii Dynamics for Bose-Einstein Condensates. Analysis & PDE 12 , no. 6 (2019).   arXiv - article
26. (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 (2015).   article

Lecture Notes

• Mathematical Quantum Mechanics with Applications.   pdf