|Sfb 288 Differential Geometry and Quantum Physics|
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.
[A1] Integrable systems in differential geometry [A2] Experimental mathematics and visualization [B1E] Spectral properties of Dirac and Laplace operators and gauge field theory [B7E] Spinor field equations and Lorentzian geometry [C1] Discrete differential geometry, quantum field theory and statistical mechanics [C2] Lattice field theory, integrable systems and quantum symmetry [C4] Differential-Geometric and Topological Methods in Discrete Geometry and Combinatorics [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