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Mathematical Sciences

Research project: Metric geometry and analysis

Currently Active: 

This group carries out research at the interface of noncommutative geometry and geometric group theory.  Our interests include: K-theory for operator algebras; C*-algebras for groups and spaces; coarse geometry; CAT(0) cube complexes; generalised homology and cohomology theories. There is a lot of cross-over and interrelation between these areas of research.

This research area is inspired by the work of Connes in non-commutative geometry and of Gromov and others in generalisations of differential geometry. Members of the group have recently established results concerning

  • the representation theory of the universal cover of SL2(R)
  • a connection between Langlands duality and the Baum-Connes correspondence
  • a generalisation of the Pimsner-Voiculescu sequence
  • asymptotic dimension of CAT(0) cube complexes
  • the boundary coarse Baum-Connes conjecture (relating the large scale K-homology of a space to the K-theory of its coarse C^* algebra)
  • Poincaré duality for algebras (introducing a new calculus for operations in Kasparov’s KK theory).

A key feature of this work is the use of the geometry of a group (or more strictly of a space on which the group acts) to construct analytic or representation theoretic invariants.

We have links with Penn State, Vanderbilt, Hawaii, Fudan and Warsaw, and recent PhD students include Ana Khukhro (Neuchatel), Martin Finn-Sell (Vienna) and Chris Cave (Copenhagen).

The group hosts a number of international visitors each year, and has recent grants from the EPSRC, the LMS, the Royal Society and the Leverhulme Trust.

Related research groups

Pure Mathematics
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