Meetings Information about the Network Mailing List

**Future
meetings:**

**Previous meetings:**

- Gregynog,
October 2004
- Oxford,
January 2004
- York,
October 2003
- Durham,
May 2003
- Warwick,
January/February 2003
- Cardiff,
November 2002
- Cambridge,
May 2002
- London,
March 2002
- Swansea,
November 2001

The
objective of this network is to bring together groups in the UK having a common
goal in pursuing the deep connections between mathematics and physics—primarily
algebraic geometry, operator algebras and quantum groups in pure mathematics
and conformal field theory, string theory and statistical mechanics in
mathematical and theoretical physics.

The
network is initially built around Alessio Corti (Cambridge), Gustav Delius (York), David Evans -
coordinator (Cardiff), Nigel Hitchin (Oxford), Shahn Majid (Queen Mary, London), Andreas Recknagel
(King's London) and Miles Reid (Warwick).

Funding by
EPSRC grant GR/R36596/01 will enable individual visits as well as informal one
or two day meetings and network workshops.

This
builds on our previous more ad hoc arrangements which include the workshop in
Warwick in September 1999, the summer programme supported by JSPS at Warwick in 2000, the Kyoto workshop in
December 2000, and more informal visits such as for the informal lecture series
given by Alastair Craw in Cardiff in May 2000.

To give
some more idea of the flavour of the network, the
following is taken from the EPSRC grant application:

The three
threads of algebraic geometry, noncommutative
geometry and conformal field theory are interwoven. Algebraic geometry and noncommutative instantons on the
one hand, and operator algebras and CFT on the other, are
related by the common use of NCG to understand singular spaces. Thus moduli spaces in algebraic geometry appear as orbifolds, while orbifolds
associated to the noncommutative torus and subfactors
play a key role in operator algebras and CFT. Algebraic geometry is a crucial
ingredient of the attempt to relate operator algebras and CFT as in the
mysterious parallel between ADE classifications of quotient singularities in
algebraic geometry, subfactors in operator algebras and modular invariant
partition functions in CFT. Noncommutative tori arise naturally in constructing compactifications
of M(atrix) theory,
conjectured to be a nonperturbative deformation of
string theory. Noncommutative world volume field
theories living on noncommutative tori
are invariant under duality transformations generated by Morita equivalence of noncommutative tori—directly
related to T-duality of perturbative string theory compactifications. Instantons on noncommutative ALE spaces (asymptotically locally Euclidean
manifolds which are the hyper-Kaehler resolution of
the orbifolds C^2/G for finite subgroups of SU(2)) is closely related to understanding the connections
between ADE classifications.

An
automated mailing list has been established for the network. For
instructions on using the list see here.

BACK TO OPERATOR ALGEBRAS AT CARDIFF