Professor
David E. Evans

Dr
Roger Behrend

Dr
Stefan Hollands

Dr
Christian Jäkel

Dr
Vincent Knight

Dr
Mathew Pugh

Miss Claire Shelly

Professor
George A. Elliott (Honorary Professor)

Professor Vaughan F.
R. Jones (Honorary Professor)

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.

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