Christian Brennecke Christian Brennecke

Prof. Dr. Christian Brennecke

Department of Mathematics
RWTH Aachen University
Pontdriesch 14-16
52062 Aachen, Germany

Office:
Email:		 257
christian.brennecke@rwth-aachen.de

About Me

Since Oct. 2026, I work as professor at the Department of Mathematics at RWTH Aachen University. Previously, I was a Bonn Junior Fellow at the Institute for Applied Mathematics at the University of Bonn and 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

Mathematical physics, analysis, probability theory, many-body quantum mechanics, classical and quantum statistical mechanics, constructive quantum field theory.

Current Teaching

In fall 2026/2027, I am teaching an introductory (block) seminar on mathematical quantum mechanics (based on B.C. Hall's book "Quantum Theory for Mathematicians"). If you're interested in participating, please contact me via email for further information.

Publications and Preprints

  1. On the Leading Order Term of the Lattice Yang-Mills Free Energy. J. Stat. Phys. 93, no. 83 (2026).   arXiv - article
  2. (with N. Behrmann, S. Rademacher) Exponential Control of Excitations for Trapped BEC in the Gross-Pitaevskii Regime. Lett. Math. Phys. 115, no. 91 (2025).   arXiv - article
  3. (with A. Schertzer) On the Replica Symmetry of a Variant of the Sherrington-Kirkpatrick Spin Glass. Electron. Commun. Probab. 30, article no. 46 (2025).   arXiv - article
  4. (with W. Kroschinsky) Derivation of the Gross-Pitaevskii Dynamics through Renormalized Excitation Number Operators. Forum Math. Sigma 13 (2025)   arXiv - article
  5. (with A. Schertzer, C. Van Dam) Spin Covariance Fluctuations in the SK Model at High Temperature. Electron. Commun. Probab. 30, article no. 9 (2025).   arXiv - article
  6. (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
  7. (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
  8. (with C. Xu, H.-T. Yau) Operator Norm Bounds on the Correlation Matrix of the SK Model at High Temperature.   arXiv
  9. (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
  10. (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
  11. 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
  12. The Low Energy Spectrum of Trapped Bosons in the Gross-Pitaevskii Regime. J. Math. Phys. 63 (2022).   arXiv - article
  13. (with H.-T. Yau) The Replica Symmetric Formula for the SK Model Revisited. J. Math. Phys. 63 (2022).   arXiv - article
  14. (with B. Schlein, S. Schraven) Bogoliubov Theory for Trapped Bosons in the Gross-Pitaevskii Regime. Ann. Henri Poincaré 23 (2022).   arXiv - article
  15. (with M. Caporaletti, B. Schlein) Excitation Spectrum for Bose Gases beyond the Gross-Pitaevskii Regime. Rev. Math. Phys. 34 , no. 09 (2022).   arXiv - article
  16. (with P. von Soosten) On the mean-field equations for ferromagnetic spin systems. Lett. Math. Phys. 111, 108 (2021).   arXiv - article
  17. (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
  18. (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
  19. (with A. Adhikari, B. Schlein) Bose-Einstein Condensation Beyond the Gross-Pitaevskii Regime. Ann. Henri Poincaré 22 (2021).   arXiv - article
  20. (with A. Adhikari) Free Energy of the Quantum Sherrington-Kirkpatrick Spin-Glass Model with Transverse Field. J. Math. Phys. 61 (2020).   arXiv - article
  21. (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
  22. (with C. Boccato, S. Cenatiempo, B. Schlein) Bogoliubov Theory in the Gross-Pitaevskii Limit. Acta Mathematica 222 , no. 2 (2019).   arXiv - article
  23. (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
  24. (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
  25. (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
  26. (with B. Schlein) Gross-Pitaevskii Dynamics for Bose-Einstein Condensates. Analysis & PDE 12 , no. 6 (2019).   arXiv - article
  27. (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
  • Introduction to Constructive Quantum Field Theory.   pdf


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