Geometry of Moduli Spaces

Japan-Britain joint research project 2000 at Warwick

sponsored by Japan Society for the Promotion of Science (JSPS)

For aims, see the page

Mon 17th Jul--Sat 12th Aug 2000

Two weeks of informal preparatory talks

During the first two weeks of the workshop in Jul, there are many other activities at Warwick
and elsewhere, and we will run at a relaxed pace to allow informal contact between the

Wed 19th Jul

10:00 M. Reid (Warwick), Resolutions of orbifold singularities (I)
11:30 Masahiko Saito (Kobe), Algebraic geometry of the Painlev\'e equations (I)

Fri 21st Jul

10:00 M. Reid, Resolutions of orbifold singularities (II)
11:30 Masahiko Saito, Algebraic geometry of the Painlev\'e equations (II)

Tue 25th Jul

10:00 H. Nakajima (Kyoto Univ.), Hilbert schemes and Kronheimer's construction of
simple singularities and its deformations and resolution via quivers
11:30 A. Craw (Warwick), McKay correspondence for finite Abelian subgroups of SL(3)

Wed 26th Jul

10:00 Yukari Ito (Tokyo Metropolitan), Quotient singularities by finite subgroups of SL(3)
2:00 W. Crawley-Boevey (Leeds), Quivers and preprojective algebras

Fri 28th Jul

10:00 Tom Bridgeland (Edinburgh), Derived categories
11:30 Fedya Bogomolov (Courant Inst.), The Szpiro conjecture and braid groups
On some of the other days, there will be opportunities for cultural activities for example, a
visit to London and a Proms concert (see
or to Stratford and the Royal Shakespeare company (see

Main workshop, Mon 31st Jul--Fri 11th Aug 2000

To simplify the task of writing the report to JSPS, all participants are requested to provide:
1. an abstract of talk;
2. preprints, papers in preparation, work in progress worked on during the conference
(bibliographical details wherever possible);
3. useful collaborations, new research ideas stimulated by the meeting;
4. anything else positive for the report.

Tue 1st Aug

11:00 Richard Thomas (Oxford and London Imperial), Derived categories and
mirror symmetry of singularities
2:00 Mark Gross (Warwick, with Pelham Wilson, DPMMS), Large complex structure
limits of K3 surfaces
4:00 Tom Bridgeland (Edinburgh), Flops and derived categories

Wed 2nd Aug

11:00  Yukari Ito (Tokyo Metropolitan), Special McKay correspondence
2:00 Akira Ishii (Kyoto), Remarks on McKay correspondence for GL(2)
4:00 W. Crawley-Boevey (Leeds), Decomposition of Marsden-Weinstein
reductions for representations of quivers

Thu 3rd Aug

11:00 Kyoji Saito (Kyoto, RIMS), Elliptic Lie algebras
2:00 Masahiko Saito (Kobe), Symmetries of affine Weyl groups and Painlev\'e
4:00 Ian Grojnowski (DPMMS, Cambridge), Rigid structure on the symmetric group

Sat 5th Aug

11:00 Shigeru Mukai (Nagoya), Bipolyhedral groups and moduli of Abelian surfaces
  lunch: sandwiches in Math Inst. (UKL4:00)
2:00 P. Slodowy (Hamburg), Loop groups, bundles over elliptic curves and simple
elliptic singularities
4:00 Miles Reid (Warwick), Where do we go from here?
  from 5:30: pub dinner The Waterman, Birmingham Road, Hatton
The Newton Institute at Cambridge has an activity on Singularity theory, see .

Mon 7th Aug

11:00 Junkai Alfred Chen (Taiwan), Some applications of Mukai-Fourier
transform on Abelian varieties (joint work with C. Hacon)
2:00 Kota Yoshioka (Kobe), Moduli space of sheaves on K3 and Abelian
4:00 Greg Sankaran (Bath, with Alastair King), Tilting bundles on toric
quiver varieties

Tue 8th Aug

11:00 Alastair King (Bath), Almost Koszul algebras
2:00 Balázs Szendröi (Warwick), Mapping class group for mirror manifolds
4:00 Alastair Craw (Warwick), Tautological line bundles on A-Hilb C^3

Wed 9th Aug

11:00 Dai Evans (Cardiff), From XY to ADE
2:00 Yasuyuki Kawahigashi (Tokyo Univ.), McKay correspondence in the
theory of subfactors
3:30 Burt Totaro (DPMMS, Cambridge), The elliptic genus of a singular variety
5:00 Richard Thomas, Mirror symmetry, Lagrangians and special

Thu 10th Aug

9:30 Gavin Brown (Oxford, with Miles Reid), Mori flips of type A
11:00 Ken-ichi Shinoda (Sophia), Coinvariant algebras of finite groups in SL(3,C)
2:00 Atsushi Takahashi (Kyoto, RIMS), Hilbert schemes and Gromow-Witten invariants
4:00 Hiraku Nakajima (Kyoto Univ.), Remarks on McKay correspondence
We may keep Fri 11th Aug free so that we can bus over to the Nute.

Currently known participants

Fedya Bogomolov (Courant) Jul 27--31
Tom Bridgeland (Edinburgh) Jul 24--Aug 7
Jungkai Alfred Chen (Taiwan) Jul 28--Aug 12
Alastair Craw (Warwick) Jul 17--Aug 22
William Crawley-Boevey (Leeds) three visits Tue--Thu of each week
David E Evans (Cardiff) Jul 31--Aug 31
Yasushi Gomi (Sophia) Jul 16--Aug 14
Ian Grojnowski (Cambridge) Jul 24--Aug 7
Mark Gross (Warwick) Jul 17--Aug 4
Martin Gulbrandsen (Oslo) Jul 17--Aug 12
Fumio Hidaka (Senshuu) Jul 16--Aug 12
Steve Humphries Jul 21--Aug 5
Akira Ishii (Kyoto) Jul 19--Aug 14
Yukari Ito (Tokyo Metro.) Jul 23--Aug 11
Yasuyuki Kawahigashi (Tokyo) Jul 20--Aug 13
Rie Kidoh (Hokkaido) Jul 16--Aug 14
Alastair King (Bath) Jul 31--Aug 12
Adrian Langer (Warszawa and Warwick) Always
Kazuhisa Maehara (Tokyo Inst. of Polytechnics) Aug 4--11
John McKay (Concordia) Aug 3--Aug 7
Shigeru Mukai (Nagoya) Aug 1--Aug 9
Hiraku Nakajima (Kyoto) Jul 23--Aug 11
Iku Nakamura (Hokkaido) will not attend
Miles Reid (Warwick) Always
Dmitry Rumynin (Warwick) Always
Kyoji Saito (Kyoto RIMS) Jul 17--Aug 10
Masahiko Saito (Kobe) Jul 14--Aug 8
Greg Sankaran (Bath) Several visits of 2--3 days
Ken-ichi Shinoda (Sophia) Jul 16--Aug 14
Bal\'azs Szendr{\H o}i (Warwick) Jul 26--Aug 9
Atsushi Takahashi (Kyoto RIMS) Jul 17--Aug 12
Richard Thomas (Imperial) Several visits
Tadashi Tomaru Jul 16--Aug 10
Burt Totaro (Cambridge) At least a few days in Aug
Andrei Tyurin Aug 3--12
Nikos Tziolas (Warwick) Always
Pelham Wilson (Cambridge) One day only Tue 1st Aug
Kota Yoshioka (Kobe) Jul 28--Aug 14
Masahiko Yoshinaga (Kyoto, RIMS) Jul 17--Aug 12