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Operator Algebras and Noncommutative Geometry


Operator Algebras and Noncommutative Geometry has become a central field in mathematics with applications and connections across mathematics and theoretical physics.

The project integrates:

  • algebra
  • analysis
  • geometry
  • topology
  • applications in and drawing inspiration from physical problems – statistical mechanics and conformal quantum field theory.

The field is important worldwide with centres in:

  • Vanderbilt
  • Berkeley
  • UCLA
  • Harvard
  • Toronto
  • Kyoto
  • Tokyo
  • Canberra
  • Sydney
  • numerous centres in Europe

The proposer has strong links with all of these – including ongoing collaborations with Gannon in Canada, Grossman at UNSW and Kawahigashi at Tokyo University.

Evans has co-ordinated two Marie Curie Research Training Networks in Europe, involving:

  • Copenhagen
  • Oslo
  • Dublin
  • Paris
  • Munster
  • Gottingen
  • Rome

with collaborators Fields Medallist Connes (College de France), Cuntz (Leibnitz Prize winner, Munster).

These networks provide ample opportunity for further collaboration. An EPSRC supported PDRA Andreas Aaserud has been recruited from UCLA – who obtained his Phd under the supervision of ICM plenary speaker Sorin Popa. Stefaan Vaes (Leuven) is the Rothschild Professor at the 6 month programme on Operator Algebras at the Newton Institute in 2017 organised by Evans, Fields Medalist Jones (Vanderbilt) and Izumi (Kyoto). Vaes will give public lectures at Cambridge and Cardiff.

These networks all give ample opportunity for collaboration.

Project aims and methods

The student will be working within the Geometry, Algebra, Mathematical Physics and Topology (GAPT) group. The group has seven permanent members. Additionally, the group currently has one EPSRC award held by the proposer supporting a PDRA, has recently hosted an EPSRC postdoctoral fellow, an ERC Starting Grant, led two EU Marie Curie Networks, and regularly organises workshops at Cardiff and elsewhere.

A 6-month programme at the Newton Institute, Cambridge, in 2017 will be led by the proposer. The prestigious Rothschild professor at that programme is based in Leuven who will give public lectures at Cambridge and Cardiff.


Professor David E Evans

Professor David E Evans

Research Professor of Mathematics

Welsh speaking
+44 (0)29 2087 4522

Programme information

For programme structure, entry requirements and how to apply, visit the Mathematics programme.

View programme
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