Mathematics Institute - University of Warwick - Coventry CV4 7AL - UK

20th - 25th September 1999

(First talk at 2:00 pm on Mon 20th September.
The final talk 12:00--1:00 on Sat 25th September)

Scientific committee: David E Evans (Cardiff), Yasuyuki Kawahigashi (Tokyo University), Iku Nakamura (Hokkaido) and Miles Reid (Warwick)

Provisional 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 possible Q&A session
buffet party in the math common room from 7:00

Wednesday 22nd September
10:00 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: (TBA Fourier Mukai ?)

Thursday 23rd September
9:30 Gannon: A conjectured list of all but finitely many Kac-Moody modular invariants
10:45 Feng Xu: Algebraic coset conformal field theory
12:00 Batyrev: Vertex algebras and mirror symmetry
free afternoon and evening (e.g. Midsummer night's dream at Stratford -- we can help organise transport, but see the box office directly about tickets)

Friday 24th September
approx 5 talks, say 10:00, 12:00, 2:00, 3:30, 5:00
Vladimir Baranovsky: TBA
P. Bouwknegt: Universal chiral partition functions
Juergen Fuchs: Chiral blocks, simple currents and extensions
7:00 Evening party in Mathematics Common Room
(or CBSO play Sibelius, Dutilleux, Mahler at Birmingham Symphony Hall)

Saturday 25th September
3 talks at 9:30, 10:45 and 12:00
Valentina Petkova: Boundary conformal field theories, ADE classification and generalizations III
(J. Graham): TBA
1:00 pub lunch

Other possible speakers:
Anda Degeratu: McKay correspondence via eta invariants
Dominic Joyce: TBA
John McKay: The ADE Dynkin diagrams: results and problems

Confirmed 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),
A. Degeratu (MIT), J. Fuchs, T. Gannon (Alberta), G. Gonzalez-Sprinberg
(Grenoble), Satoshi Goto (Sophia Univ, Tokyo), J. Graham (Imperial),
M. Gross (Warwick), K. Hannabuss (Oxford), Y-H. He (MIT),
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), K-i. Shinoda (Sophia U., Tokyo),
Jun S. Song (MIT), S. Stratila (Bucharest), B. Szendroi (Warwick),
Bruce Westbury (Warwick), Feng Xu (Oklahoma), Jean-Bernard Zuber (Saclay)

British participants (expected some of the time):
Bill Crawley-Boevey (Leeds), Ian Grojnowski (DPMMS, Cambridge), N.J. Hitchin
(Oxford), D. Joyce (Oxford), Nick Shepherd-Barron (DPMMS, Cambridge),
P.M.H. Wilson (DPMMS, Cambridge)

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.

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

Further information
Details of the lecture schedule will be posted on the web when available.

For other information, please contact:
Peta McAllister - MRC Business Manager -

Accommodation Form:
Please e-mail to
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Report on Workshop to EPSRC
For further information on any of the above contact:
Peta McAllister - MRC Business Manager -
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