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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