Noncommutative Geometry and Operator Algebras at Cardiff

People and Overview of the Group


Professor David E. Evans
Dr Roger Behrend
Dr Vincent Knight
Dr Mathew Pugh
Dr Timothy Logvinenko
Dr Gandalf Lechner

Mr Stephen Moore
Mr Cellan White

Professor George A. Elliott (Honorary Professor)
Professor Vaughan F. R. Jones (Honorary Professor)

Overview of the Group

The group is led by David Evans and has a broad sweep of interests in operator algebras, noncommutative geometry and their applications and connections to other mathematical areas and physics including K-theory, E-theory, quantum groups in pure mathematics and statistical mechanics, algebraic, conformal, topological quantum field theories in mathematical and theoretical physics.

David Evans has published with Yasuyuki Kawahigashi a monograph Quantum Symmetries on Operator Algebras the combinatorial and physical aspects of operator algebras (see here for the list of updates/corrections). This is a continuation of the work of Evans in his previous collaborations with Araki and Lewis on a C*-algebra approach to phase transitions in the two-dimensional Ising model. Evans is also currently interested in the study of amenable C*-algebras by K- theoretic or topological invariants, e.g. the expression of finite amenable simple C*- algebras as the inductive limit of simpler building blocks - Elliott and Evans expressed the irrational rotation algebras as inductive limits of circle algebras. There is much interchange of ideas from amenable subfactors and amenable C*-algebras in this work (e.g. through common ideas from orbifolds and Rokhlin properties of automorphisms).

Roger Behrend has worked on exactly solvable statistical mechanical lattice models and associated conformal field theories, and in particular has considered the application of nontrivial boundary conditions to such systems.  This has involved finding solutions to the boundary Yang-Baxter equation, classifying boundary conditions and studying relationships between bulk and boundary properties.

David Evans is a member of EPSRC's Mathematics College (1995-1997, 1997-1999, 2003-2005) and is a member of the University of Warwick Mathematics Research Centre Steering Committee (2000-2003).

There is currently one graduate student associated with the group: Claire Shelly.

Cardiff is a member of the EU Network in Noncommutative Geometry. We also interact with algebraic geometers, particularly Miles Reid at Warwick and the COW Seminar, and boundary conformal field theorists.

On 1 May 1998, the Operator Algebras Group moved from Swansea to Cardiff. Since 1987, the following have at various periods been members of the group as postdoctoral fellows (funded by EPSRC, EU, the University of Wales, and the GB-Sasakawa foundation):

1 T. Loring (Ph.D. Berkeley 1986)
2 T. Matsui (Ph.D. Kyoto 1985)
3 E.G. Beggs (D.Phil. Oxford 1988)
4 S. Majid (Ph.D. Harvard 1988)
5 T. Yamanouchi (Ph.D. UCLA 1990)
6 M. Izumi (Ph.D. RIMS, Kyoto)
7 H. Su (Ph.D. Toronto 1992)
8 M. Nazarov (Ph.D. Moscow 1988)
9 A. Recknagel (Ph.D. Bonn 1993)
10 T. Isola (Ph.D. Rome 1993)
11 F.P. Boca (Ph.D. UCLA 1994)
12 J. Bockenhauer (Ph.D. Hamburg 1996)
13 S. Winkler (Ph.D. UCLA 1996)
14 S. Goto (Ph.D. Tokyo Univ. 1996)
15 P. Goldstein (Ph.D. Wales 1997)
16 R. Behrend (Ph.D. Melbourne 1997)
17 S. Neshveyev (Ph.D. Kharkov 1999)
18 I. Zois (D.Phil. Oxford)
19 R. Popescu (Ph.D. Lyon)
20 P. S. Chakraborty (Ph.D. Kolkatta)
21 A. Agostnini (Ph.D. Naples)
22 J. Fjelstad (Ph D Karlstad)

23 P. Grossman (Phd Berkeley)

Masaki Izumi went from Swansea to a Miller Fellowship at Berkeley, and in September 1996 took up a permanent position at Tokyo University. In April 1999, he moved to Kyoto University. The Mathematical Society of Japan created in 1996 a new prize for young Japanese mathematicians, the Takebe prize. Masaki Izumi was selected as one of the first winners of this prize. Take Yamanouchi left for a tenured position with David Evans' collaborator Akitaka Kishimoto in Hokkaido whilst Taku Matsui moved in April 1997 from Tokyo Metropolitan University to a full professorship at Kyushu University. Terry Loring was a postdoc at Dalhousie after leaving Swansea, and is now an Associate Professor at Albuquerque. Shahn Majid has subsequently held an EPSRC Advanced Fellowship at Cambridge and a Royal Society Postdoctoral Fellowship there. In September 1999, he moved to a readership at QMW, London. Hongbing Su was partially supported by a Canadian NSERC fellowship whilst here, and then became a postdoctoral fellow at the Fields Institute for Research in the Mathematical Sciences in Toronto. Andreas Recknagel moved from Swansea to an EU postdoctoral fellowship at ETH Zurich, followed by postdoc positions at IHES, Paris and Potsdam, Germany. In September 2000, he became a lecturer at King's College, London. Max Nazarov has moved to York. Tommaso Isola has a permanent position in Rome (Tor Vergata).

The Operator Algebras group is the hub for the live video seminar network linking the 4 campuses of the University of Wales. Since 1992, there have been regular seminars on mathematical physics - which are recorded on video tape.