MATHEMATICS
RESEARCH
CENTRE
WORKSHOP ON
MODULAR INVARIANTS, OPERATOR ALGEBRAS,
&
QUOTIENT SINGULARITIES

20th - 25th September 1999
Scientific committee: David E Evans (Cardiff), Yasuyuki Kawahigashi (Tokyo University), Iku Nakamura (Hokkaido) and Miles Reid (Warwick)

Program

Monday 20th September
Morning: registration, coffee

2:00 Terry Gannon: An introduction to modular invariants
3:30 Miles Reid: Quotient singularities
5:00 Yasuyuki Kawahigashi: An introduction to subfactors

Tuesday 21st September
10:00 Hiraku Nakajima: Quiver varieties
12:00 David Evans: Modular invariants and subfactors I
2:00 Jean-Bernard Zuber: Boundary conformal field theories, ADE classification and generalizations I
4:00 Iku Nakamura: Hilbert scheme of G-orbits and representations of G
5:30 Q&A session

Wednesday 22nd September
10:00 Jens Bockenhauer: Modular invariants and Subfactors II
12:00 Yukari Ito: Crepant resolution and the McKay correspondence
2:00 Paul Pearce: Boundary conformal field theories, ADE classification and generalizations II
4:00 Tom Bridgeland: McKay correspondence via Fourier-Mukai transformations

Thursday 23rd September
9:30 Terry Gannon: A conjectured list of all but finitely many Kac-Moody modular invariants
10:45 Feng Xu: Algebraic coset conformal field theory
12:00 Victor Batyrev: Vertex algebras and mirror symmetry

Friday 24th September
10:00 Vladimir Baranovsky: Moduli spaces and convolution algebras
12:00 Peter Bouwknegt: Universal chiral partition functions
2:00 Juergen Fuchs: Chiral blocks, simple currents and extensions
3:30 Alastair King: Pre-projective algebras
5:00 John Graham: Temperley-Lieb algebras of types A, D and E

Saturday 25th September
9:30 Valentina Petkova: Boundary conformal field theories, ADE classification and generalizations III
10:45 Philippe Ruelle: Fermat curves and SU(3) modular invariants
12:00 John McKay: ADE, old results and new challenges

Participants:
M. Asaeda (Penn State), V. Batyrev (Tuebbingen), F. Boca (Cardiff), J. Boeckenhauer (Cardiff), P. Bouwknegt (Adelaide), T. Bridgeland (Edinburgh), Roger Carter (Warwick), A. Coste (Orsay), A. Craw (Warwick), Bill Crawley-Boevey (Leeds), A. Degeratu (MIT), J. Fuchs (ETH, Zuerich), T. Gannon (Alberta), G. Gonzalez-Sprinberg (Grenoble), Satoshi Goto (Sophia Univ, Tokyo), J. Graham (Imperial), Ian Grojnowski (DPMMS, Cambridge), M. Gross (Warwick), K. Hannabuss (Oxford), Y-H. He (MIT), N.J. Hitchin (Oxford), Y. Ito (Tokyo Metropolitan Univ), A. King (ICTP, Trieste), J. McKay (Concordia, Montreal), T. Matsui (Kyushu), J. Moody (Warwick), H. Nakajima (Kyoto Univ), R. Nest (Copenhagen), A. Paolucci (Torino), P Pearce (Melbourne), V. Petkova (Sofia), P. Pinto (Cardiff), P. Ruelle (Orsay), Dmitry Rumynin (Warwick), Nick Shepherd-Barron (DPMMS, Cambridge), K-i. Shinoda (Sophia U., Tokyo), Jun S. Song (MIT), S. Stratila (Bucharest), B. Szendroi (Warwick), Bruce Westbury (Warwick), P.M.H. Wilson (DPMMS, Cambridge), Feng Xu (Oklahoma), Jean-Bernard Zuber (Saclay)

Scientific programme
The workshop brings together specialists in operator algebras, statistical mechanics, conformal field theory and algebraic geometry to explore recently observed connections between different approaches to the algebra and geometry of finite subgroups of SU(2) and SU(3). On the face of it, II_1 and III_1 subfactors in operator algebras, modular invariant partition functions in conformal field theory, finite subgroups of SU(n) and the resolution of their orbifolds are more-or-less unrelated topics. Nevertheless their study leads to combinatorics displaying all kinds of analogies. Our SU(2) cases, along with many other areas of mathematics are governed by the ADE classification. Recent work in trying to understand the higher rank case, so far mainly SU(3), involves induction of sectors in nets of subfactors, the classification of conformal boundary conditions, cohomology of the resolution of a singularity - all of which provide fusion graphs generalising the ADE classification. The main objective of this workshop is to probe for connections at a deeper level to explain the empirically observed similarities between the results. We expect this to lead to progress in solving open problems.

Money
The conference is sponsored by EPSRC, with generous contributions from JSPS and other Japanese research funds, and from the Royal Society. We can also use a small grant from the LMS to cover UK participants. Our funding is limited, and we will have to ask many participants to cover their travel and living expenses from other sources, but please write if you think you deserve expenses. Those interested in taking part should write to peta@maths.warwick.ac.uk

Further information
Details of the lecture schedule will be posted on the web when available.
www.maths.warwick.ac.uk/research/index.html

For further information on any of the above contact:
Peta McAllister - MRC Business Manager - peta@maths.warwick.ac.uk