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