Sfb 288 Differential Geometry and Quantum Physics |
Research
The research at the Sfb falls within 5 main areas of interest:
- Differential Geometry and Classical Mechanics
- Integrable systems in differential geometry
- Experimental mathematics and visualization (some individual projects)
- Elliptical Operators in Geometry and Physics
- Spectral properties of Dirac and Laplace operators and gauge field theory
- Geometric variational problems
- Discretization in Geometry and Physics
- Discrete differential geometry, quantum field theory and statistical mechanics
- Lattice field theory, integrable systems and quantum symmetry
- Analysis of Quantum Mechanical Systems
- Semi classical analysis: Born-Oppenheimer approximation, dynamics in mean field models, the large atom limit and the adiabatic theorem
- Quantum mechanical models
- Spectral theory of gauge-periodic operators
- Spectral invariants of singular manifolds and their deformation properties
- Classical and quantum mechanical inverse problem of periodic potentials
- Geometry and Algebraic Quantum Field Theory
- Geometry, algebraic quantum field theory and the form factor programme