Thematic program "L²-invariants and their analogues in positive characteristic"  

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The thematic program will be devoted to recent developments of the theory of L²-invariants and their analogues in positive characteristic.  

Historically, the theory of L²-invariants has its origen in a work of M. Atiyah, where he proposed an extension of the Atiyah-Singer index theory of elliptic differential operators on compact manifolds to the non-compact case. The modern definition of these invariants is more algebraic and uses the language of CW-complexes. The analogue of the first L²-Betti number in positive characteristic, the p-gradient, was introduced by M. Lackenby in his study of hyperbolic 3-manifold groups.  

The study of L²-invariants is linked to topology, geometry, global analysis, operator theory, ring theory, group theory and K-theory. This program aims to reunite leading specialists on these areas in an exciting research environment at the ICMAT. There will be a school and several advanced courses on recent develoments of the area. This program is a great opportunity to train young researchers on an area which has been successful in the study of important problems as the Baum-Connes conjecture or the Hanna Neumann conjecture, and it is important source of tools and ideas for attacking very interesting open problems.

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