Objective
Algebraic K-theory is a strong international area of activity, with both hard problems and interaction with many areas of mathematics, for example cohomology and classical groups. NIS research teams are particularly strong in this area, and exchanges between NIS and West European participants will strengthen research in these fields.
The application of categorical methods has become stronger over recent years, and is expected to produce new methods and results in homological algebra and K-theory. Two newer aspects are non-abelian methods, the use of internal groupoids and their higher dimensional generalizations for local-to-global problems and the realization that these enhance computational aspects.
This project will stimulate interaction between these areas and will form a basis for future collaboration. It is expected that some of the conjectures in the field of K-theory will be resolved, as detailed above. In local-to-global methods and internal groupoids, new relations are expected between generalised van Kampen theorems, the theory of descent and the notions of holonomy and monodromy groupoids which arise in differential topology. In non-abelian homological algebra new tools are expected in the shape of constructions of tensor products of forms of crossed complexes (for example, in the area of commutative algebra) and also the notion of crossed differential algebra in these contexts.
Topic(s)
Call for proposal
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LL57 1UT Bangor
United Kingdom