SFB 878:  Groups, Geometry and Actions

• Subject Area: Mathematics
• Term: from 2010 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 129719356

In the Collaborative Research Center 878, various disciplines of mathematics are combined to investigate fundamental questions and problems about groups, geometry, actions and their interplay.Geometric objects are ubiquituous, in real life as well as in mathematics. The concept of a group, even though more difficult to visualize, is another fundamental concept of modern mathematics. It serves as a tool to structure complex information, for example by describing symmetries or the transformations of a geometric object. The focus of CRC 878 is the study of groups and (in a broad sense) geometrically defined mathematical structures as well as their interplay via actions. Our project encompasses a very broad spectrum of modern geometric methods ranging from classical differential geometry over topology and algebraic geometry to non-commutative geometry and model theory. In each of these fields, not only do group actions play a prominent role for the understanding of the geometric objects but, conversely, the methods of these areas can be used to study the structure of groups and their representations. Here, a representation of a group means that the group is describing transformations of some mathematical structure, for example as a group of isometries in differential geometry, as a homotopy group in topology or as a Galois group in number theory.

• DFG Programme: Collaborative Research Centres

Completed projects

• A01 - Algebraic vector bundles (Project Head Deninger, Christopher )
• A02 - p-adic group algebras (Project Heads Scherotzke, Sarah ;  Schneider, Peter )
• A03 - Moduli spaces of G-Shtukas and the Langlands Program (Project Head Hartl, Urs )
• A04 - Groups, geometries and model theoretic modularity (Project Head Tent, Katrin )
• A05 - Abstract classification theory: topological spaces, groups, and descriptive set theory (Project Heads Schindler, Ralf ;  Tent, Katrin )
• A06 - Definable reducibility (Project Heads Miller, Benjamin ;  Schindler, Ralf )
• A07 - Generalized cohomology theories and applications to algebraic and arithmetic geometry (Project Heads Cuntz, Joachim ;  Deninger, Christopher ;  Nikolaus, Thomas )
• A08 - Derived categories, quasi-hereditary algebras, and toric geometry (Project Heads Hille, Lutz ;  Schürmann, Jörg )
• A09 - Model theory of valued fields and definable groups (Project Heads Hils, Martin ;  Jahnke, Franziska ;  Tent, Katrin )
• B01 - Singular metric spaces and foliations (Project Head Wilking, Burkhard )
• B02 - Geometric evolution equations (Project Heads Böhm, Christoph ;  Wilking, Burkhard )
• B03 - Geometry of scalar curvature (Project Head Lohkamp, Joachim )
• B04 - Reductive groups and combinatorial structures (Project Head Kramer, Linus )
• B05 - K-theory, L-theory and assembly maps (Project Heads Bartels, Arthur ;  Lück, Wolfgang ;  Weiss, Michael )
• B06 - Equivariant homotopy and homology (Project Head Lück, Wolfgang )
• B07 - Measurable group theory and L2-invariants (Project Heads Löh, Clara ;  Lück, Wolfgang ;  Sauer, Roman )
• B08 - Symplectic Geometry-Theory and Applications to Dynamics (Project Heads Albers, Peter ;  Witt, Frederik )
• B09 - Cobordism categories and geometric topology (Project Heads Ebert, Johannes ;  Weiss, Michael )
• C01 - Dynamical Systems from a noncommutative point of view (Project Heads Cuntz, Joachim ;  Echterhoff, Siegfried ;  de Laat, Ph.D., Tim ;  Winter, Wilhelm )
• C02 - The fine structure of nuclear C*-algebras (Project Heads Cuntz, Joachim ;  Winter, Wilhelm )
• C03 - Baum-Connes conjecture and expanders (Project Heads Cuntz, Joachim ;  Echterhoff, Siegfried ;  de Laat, Ph.D., Tim ;  Winter, Wilhelm )
• C04 - Mathematical aspects of QFT and condensed matter (Project Heads Bellissard, Jean ;  Wulkenhaar, Raimar )
• C05 - Random walks, branching, random media (Project Heads Alsmeyer, Gerold ;  Dereich, Steffen ;  Gantert, Nina Jael ;  Mukherjee, Chiranjib )
• C06 - Iterated Function Systems, Random Analytic Functions and Random Matrices (Project Heads Deninger, Christopher ;  Kabluchko, Zakhar ;  Löwe, Matthias )
• MGK - Integrated Research Training Group (Project Heads Hartl, Urs ;  Löwe, Matthias ;  Tent, Katrin )
• Z - Central tasks (Project Heads Cuntz, Joachim ;  Deninger, Christopher ;  Lück, Wolfgang ;  Schneider, Peter ;  Tent, Katrin )

• Applicant Institution: Universität Münster
• Participating Institution: Max-Planck-Institut für Mathematik
• Spokespersons: Professor Dr. Christopher Deninger, from 10/2010 until 11/2010; Professor Dr. Wolfgang Lück, until 9/2010; Professorin Dr. Katrin Tent, since 11/2010