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From SFB1085 - Higher Invariants

Jump to navigationJump to searchThe **SFB 1085 Higher Invariants** at the Faculty of Mathematics at the Universität Regensburg is funded by the DFG. The SFB offers:

- postdoc and PhD positions Apply Now!
- an extensive and flexible guest programme Apply Now!

## 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.