Department of Mathematics

JProf. Dr. Shahnaz Farhat

Contact Information

Universität Tübingen
Fachbereich Mathematik
AB Mathematische Physik
Auf der Morgenstelle 10
72076 Tübingen 

Room: C4 P34
Tel: +49 (0)7071 29 78672
E-Mail: shahnaz.farhat at uni-tuebingen.de
 

Teaching

WS 2026/27

SS 2026

  • International Mathematics Competition Training

Research Interests

My research lies in mathematical physics, at the interface of partial differential equations, functional analysis, probability, and quantum many-body theory. I am particularly interested in semiclassical and multiscale analysis, transport and kinetic equations, quantum many-body systems, equilibrium and Gibbs states, and mean-field limits.

Current Research

My current research focuses on semiclassical analysis, equilibrium and Gibbs states, quantum many-body systems, and mean-field approximations. A central theme is the rigorous derivation of effective macroscopic or classical descriptions from microscopic quantum models, both in dynamical and equilibrium settings.


Publications

  • Invariant measures as probabilistic tools in the analysis of nonlinear ODEs and PDEs (2022)
    With Zied Ammari and Vedran Sohinger.
    Published in the Springer INDAM Series proceedings.

  • A paradigm for the creation of scales and phases in nonlinear evolution equations (2022)
    With Christophe Cheverry.
    Published in the Electronic Journal of Differential Equations.

  • Long-time gyrokinetic equations (2023)
    With Christophe Cheverry.
    Published in the Quarterly of Applied Mathematics.

  • Almost sure existence of global solutions for general initial value problems (2023)
    With Zied Ammari and Vedran Sohinger.
    Published in Advances in Mathematics.

  • Quantum-classical motion of charged particles interacting with scalar fields (2024)
    Published in the Journal of Mathematical Physics (Editor’s Pick).

  • Expansion of the Many-body Quantum Gibbs State of the Bose–Hubbard Model on a Finite Graph (2024)
    With Zied Ammari and Sören Petrat.
    Published in Documenta Mathematica.

  • Mean-Field Dynamics of the Bose–Hubbard Model in High Dimension (2025)
    With Denis Périce and Sören Petrat.
    Accepted, to appear in Annales Henri Poincaré.
    arXiv:2501.05304

  • Ground state energy of the Bose–Hubbard model with large coordination number with a polaron-type quantum de Finetti theorem (2026)
    With Denis Périce and Sören Petrat.

    arXiv:2603.29562

  • A perturbative microscopic derivation of the focusing (\Phi^6_1) measure with rough cut-off (2026)
    With Andrew Rout.

    arXiv:2607.20400