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The SFB 1085 Higher Invariants at the Faculty of Mathematics at the Universität Regensburg is funded by the DFG.
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Speaker

• Speaker: Prof. Dr. Guido Kings
• Cospeaker: Prof. Dr. Ulrich Bunke
• Coordinator: Birgit Tiefenbach, office M 301, phone +49 (0)941-943-5871
• email sfb-higher-invariants@mathematik.uni-regensburg.de

Topics

Invariants play a dominant role in all of mathematics: Invariants should be fine enough to extract the right information, but coarse enough to be computable in specific cases. Higher invariants are a structural and hierarchical refinement of certain classical invariants. The long term goal of this Collaborative Research Centre is to formulate the principles of construction and computation of higher invariants in a systematic way.

• Higher Chern classes
• Volumes, L-functions, and polylogarithms
• Metric structures on cohomology, vector bundles, and cycles
• Higher categories and enriched structures

Projects and principal investigators

• Cohomology of Higher-Dimensional Schemes {Ended} (U.Jannsen, M. Kerz)
• Differential Arithmetic Geometry {Ended} (U. Bunke, G. Kings, G. Raptis, G. Tamme)
• Cycle Classes in p-Adic Cohomology (V. Ertl, M. Kerz)
• Topological Aspects of Curvature Integrals (B. Ammann, C. Löh)
• Tropical Approaches to Arakelov Theory (W. Gubler, K. Künnemann)
• Coarse Homotopy Theory (U. Bunke, D.-C. Cisinski)
• Higher Nearby Cycles Functors and Grothendieck Duality (D.-C. Cisinski, M. Hoyois)
• Derivators in Higher Category Theory {Ended} (D.-C. Cisinski, G. Raptis)
• Higher Categories of Correspondences {New} (D.-C. Cisinski, M. Hoyois, C. Scheimbauer)
• Motivic Homotopy Theory and Intersection Theory {New} (D.-C. Cisinski, M. Hoyois, M. Kerz)
• Spectral Algebraic Geometry (N. Naumann)
• K-Theory, Polylogarithms and Regulators (G. Kings, J. Sprang, V. Ertl)
• Simplicial Volume and Bounded Cohomology (S. Friedl, C. Löh)
• The l1-Seminorm on Homology and L2-Torsion {Ended} (S. Friedl)
• Non-Archimedean Pluri-Potential Theory (W. Gubler, K. Künnemann)
• Higher Structures in Functorial Field Theory {New} (M. Ludewig, C. Scheimbauer)
• Index Theory on Submanifold Complements {New} (B. Ammann, U. Bunke, M. Ludewig)

Miscellaneous

The CRC provides an internal research training group for PhD students and postdocs. Additionally, the CRC supports gender equality and family friendly measures for its members.