Sfb 288 Differential Geometry and Quantum Physics

Objectives

Begin of grant: 1992

Participating divisions: Differential geometry, mathematical physics

Envisaged program : Various branches within global analysis, differential geometry and topology experienced great stimulation by dealing with problems coming from mathematical physics. Vice versa theoretical physics makes more and more use of concepts and methods taken from current areas of research within differential geometry. The Sonderforschungsbereich 288 shall provide a framework for a beneficial collaboration of mathematicians and physicists in this field. In this context the stress will be laid upon:

a)	Application of quantum field theory to the geometry and topology of lower dimensional manifolds. Vice versa: geometric methods in quantum field theory.
b)	Geometry of hamiltonian systems (including infinite dimensional), applications thereof in differential geometry. Semiclassical analysis of the corresponding quantum systems.
c)	Global analysis on manifolds and spectral theory of quantum mechanical systems.

Projects:

[A1]	Integrable systems in differential geometry
[A2]	Experimental mathematics and visualization
[B1E]	Spectral properties of Dirac and Laplace operators and gauge field theory
[C1]	Discrete differential geometry, quantum field theory and statistical mechanics
[C2]	Lattice field theory, integrable systems and quantum symmetry
[D2]	Semi classical analysis: Born-Oppenheimer approximation, dynamics in mean field models, the large atom limit and the adiabatic theorem
[D5]	Quantum mechanical models
[D6E]	Spectral theory of gauge-periodic operators
[D7E]	Spectral invariants of singular manifolds and their deformation properties
[F1]	Geometry, algebraic quantum field theory and the form factor programme