Meetings
Information
about the Network Mailing
List
Future
meetings:
Previous
meetings:
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