GRK 2240:
Algebro-geometric Methods in Algebra, Arithmetic and Topology

Mathematisches Institut Heinrich-Heine-Universität Universitätsstr. 1
40225 Düsseldorf

Fachbereich Mathematik und Informatik
Bergische Universität Wuppertal
Gaußstr. 20
42119 Wuppertal

Research Aims:

The main goal of the research training group Algebro-Geometric Methods in Algebra, Arithmetic and Topology is the application of tools and results from Algebraic Geometry to pure mathematics, for instance in nearby areas of Algebraic Topology, Group Theory, K-theory, Model Theory, Number Theory and Representation Theory. Usage of these sophisticated and powerful tools will by taught systematically to our doctoral researchers. The following project titles illustrate the broad range of applications we have in mind:


1. Algebro-geometric loops and wild quotient singularities (Rülling, Schröer)
2. Chow-Witt rings and refined enumerative geometry (Wendt, Zibrowius)
3. (Chow-)Witt groups of classifying spaces and cohomology operators (Hornbostel, Zibrowius)
4. Clifford theory to calculate zeta functions of various pro-p groups (Klopsch, Späth)
5. Invariants of singularities of quiver moduli spaces (Halupczok, Reineke)
6. Cohomology and geometry of Deligne-Lusztig varieties and character sheaves (Orlik, Späth)
7. Local-analytic motivic integration (Halupczok, Orlik)
8. ℓ² cohomology of S-arithmetic groups and the rank gradient of profinite groups (Kammeyer, Klopsch)
9. Singular and arithmetic Fano varieties and quiver moduli spaces (Reineke, Schröer)
10. Stratified mixed Tate motives in p-adic analytic geometry (Orlik, Wendt)
11. Suslin homology and Chow-Witt groups with modulus (Hornbostel, Rülling)
12. Torsion growth in homology and volumes of threefolds (Kammeyer, Wendt)
13. Zeta functions for quiver representations (Klopsch, Reineke)
14. D-modules and locally analytic representations (Orlik, Schmidt)
15. Dimensions and representation growth of p-adic Lie groups (Klopsch, Schmidt)

Responsible for the content: E-Mail sendenLucas Ruhstorfer/Jens Hornbostel