SFB 478:  Geometric structures in mathematics

• Subject Area: Mathematics
• Term: from 1998 to 2009
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 5482091

In mathematics there are certain structures of a universal nature which appear in completely different settings. Understanding them allows to treat seemingly unrelated problems with uniform methods. The collaborative research centre concentrates on geometric structures, their developement as a method and their applications. This concerns fields like Arithmetic Geometry, Differential Geometry, Topology, Analysis and Noncommutative Geometry.Examples of such methods are cohomology and K-theories. They play an important role in every "Projektbereich" of the collaborative research centre. K-theory came from algebraic geometry and topology. Later this theory influenced analysis on manifolds via index theory and now has become one of the main tools in Noncommutative Geometry. Via regulators, special L-values and the theory of motives K-theory now plays an important role in Arithmetic Geometry as well. The collaborative research centre works on a number of the main open problems in mathematics like the Bloch-Kato conjectures, The Baum-Connes conjectures, conjectures of Atiyah, Hopf, Singer and many others. Work on these problems will create a lot of new and interesting mathematics which in turn will help to solve further problems. The intertwining of different mathematical directions via geometric structures will remain a fruitful line of research for a long time to come.

• DFG Programme: Collaborative Research Centres
• International Connection: USA

Completed projects

• A01 - Motives and analytic-topologocal methods (Project Head Deninger, Christopher )
• A02 - Motives, Vector bundles, p-adic methods (Project Head Deninger, Christopher )
• A3 - Modulformen, Geometrie des Laplace-Operators und Anwendungen (Project Head Elstrodt, Jürgen )
• A4 - Quadratische Formen und algebraische Varietäten (Project Head Scharlau, Winfried )
• A05 - Moduli of representations (Project Head Reineke, Markus )
• B01 - Curvature and Topology (Project Head Wilking, Burkhard )
• B02 - L²-invariants (Project Head Lück, Wolfgang )
• B3 - Gebäude (Project Head Schneider, Peter )
• B04 - Isomorphism Conjecture in algebraic K- and L-theory (Project Head Lück, Wolfgang )
• B05 - Collapsing and Metric Geometry (Project Head Wilking, Burkhard )
• B06 - Geometric bordism invariants (Project Head Dessai, Anand )
• B07 - Minimal Hypersurfaces and Scalar Curvature (Project Head Lohkamp, Joachim )
• B08 - Large-scale structure of reductive groups and buildings (Project Head Kramer, Linus )
• C01 - Rigid and formal geometry, Néron models (Project Head Bosch, Siegfried )
• C02 - Cohomological and topological methods (Project Head Bosch, Siegfried )
• C03 - Continuous representation theory of p-adic groups (Project Head Schneider, Peter )
• C04 - Buildings (Project Head Schneider, Peter )
• C05 - The arithmetic of period domains and local shtuka (Project Head Hartl, Urs )
• C06 - Groups, Buildings and Model Theory (Project Head Tent, Katrin )
• D2 - Metrische Eigenschaften und Deformationen singulärer Räume (Project Head Bröcker, Ludwig )
• E01 - Cyclic Theory and K-Theory for Locally Convex Algebras (Project Head Cuntz, Joachim )
• E02 - Bivariant K-theory and the Baum-Connes-conjectures (Project Head Echterhoff, Siegfried )
• E03 - C*-algebras (Project Head Cuntz, Joachim )
• E04 - Noncommutative geometry and quantisation of physical interactions (Project Head Wulkenhaar, Raimar )
• N - Homotopische Algebra und ihre Anwendungen (Project Head Schwede, Stefan )
• N01 - Alexandrow geometry and its applications (Project Head Petrunin, Anton )
• NWG - Alexandrov geometry and its applications (Project Head Petrunin, Anton )
• Z - Sekretariat, Einladungen, Haushaltsführung, SFB-Kolloquien und -Symposien, Gäste, Computerwartung (Project Head Deninger, Christopher )

• Applicant Institution: Universität Münster
• Spokesperson: Professor Dr. Christopher Deninger