Many-body quantum physics
- Generalised Bogoliubov transformations for interacting bosonic and fermionic systems
- Hartree–Fock–Bogoliubov theory beyond mean-field
- Spin-wave theory and its corrections in frustrated magnetic systems
- BCS–BEC crossover and attractive Hubbard models
Quantum field theory
- BPHZ renormalization and Zimmermann's forest formula
- Wightman axioms and the Osterwalder–Schrader reconstruction
- Operator product expansions in conformal field theory
- Effective field theories and their matching at low energies
Statistical mechanics & kinetic theory
- BBGKY hierarchy and truncation strategies
- Derivation of hydrodynamic equations from microscopic reversible dynamics
- Quantum kinetic equations beyond the Boltzmann approximation
- Fluctuation–dissipation relations out of equilibrium
Mathematical physics
- Spectral theory of operators arising in many-body problems
- Functional-integral methods and their rigorous justification
- Non-perturbative bounds on ground-state energies