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.