The group's research interests lie in the areas of analysis, geometry, operator theory, algebra and mathematical physics. Research topics include:
- Algebraic methods for renormalization in quantum field theory (Hopf algebras, pre-Lie and post-Lie algebras)
- Analytic methods for renormalization
- Analytic index theory
- Gauge field theories and integrable field theories
- Geometric methods for quantum field theory (groupoids, infinite dimensional geometry)
- Microlocal analysis and pseudodifferential operators
- Multizeta functions
- (Perturbative) algebraic quantum field theory
- Rough paths and regularity structures
- Zeta function and other regularization methods
