Summer School on Preprojective Algebras – Program (very preliminary)
Here you can find a schedule of the summer school.
| Tuesday |
|
|
| 08:00 - 09:00 |
Breakfast |
|
| 09:00 - 10:00 |
Talk 4: Module Varieties I
|
T. Raedschelders
|
| 10:00 - 10:30 |
Coffee break |
|
| 10:30 - 11:30 |
Talk 5: Module Varieties II
|
M. Möller
|
| 11:40 - 12:40 |
Talk 6: Rigid Modules
|
C. Ricke
|
| 12:40 - 13:30 |
Lunch |
|
| 13:30 - 14:30 |
Talk 7: Frobenius Categories
|
R. Reischuk
|
| 14:40 - 15:40 |
Talk 8: Cohen-Macaulay rings and maximal Cohen- Macaulay modules (MCM)
|
A. Zvonareva
|
| 15:40 - 16:10 |
Coffee break |
|
| 16:10 - 17:10 |
Talk 9: Kleinian Singularities & Auslander's algebraic McKay Correspondence
|
C. Aquilino
|
| 19:00 |
Dinner |
|
| Thursday |
|
|
| 08:00 - 09:00 |
Breakfast |
|
| 09:00 - 10:00 |
Lecture Series by R.O. Buchweitz - Part 2 - tba
|
|
| 10:00 - 10:30 |
Coffee break |
|
| 10:30 - 11:30 |
Talk 12: Graded Matrix Factorisations |
G. Stevenson
|
| 11:40 - 12:40 |
Talk 13: Kleinian singularities and cluster categories
|
A. Chan
|
| 12:40 - 13:30 |
Lunch |
|
| 13:30 - 14:30 |
Talk 14: Hochschild (Co-)Homology I |
H. Franzen
|
| 14:40 - 15:40 |
Talk 15: Hochschild (Co-)Homology II
|
J. Steen
|
| 15:40 - 16:10 |
Coffee break |
|
| 16:10 - 17:10 |
Talk 16: Deformations of Kleinian Singularities
|
J. Sauter
|
19:00
|
Dinner
|
|
| Friday |
|
|
| 08:00 - 09:00 |
Breakfast |
|
| 09:00 - 10:00 |
Lecture Series by R.O. Buchweitz - Part 3 - tba
|
|
| 10:00 - 10:30 |
Coffee break |
|
| 10:30 - 11:30 |
Talk 17: Coherent Sheaves, Serre Construction / "Serre's Theorem" I
|
P. Lampe
|
| 11:40 - 12:40 |
Talk 18: Coherent Sheaves, Serre Construction / "Serre's Theorem" II
|
A. van Roosmalen
|
| 12:40 - 13:30 |
Lunch |
|
References:
There are several references. When suggesting a talk you will be told
which are the ones relevant for you.
[BGL]
D. Baer, W. Geigle and H. Lenzing, The preprojective algebra of a tame
hereditary Artin algebra, Communications in Algebra 15 (1987), 425--457.
[BIRS] A.B. Buan, O. Iyama, I. Reiten and J. Scott, Cluster structures
for 2-Calabi-au categories and unipotent groups, Compositio Math.
145 (2009), 1035--1079.
[CB-H] W. Crawley-Boevey and M. Holland, Noncommutative Deformations of Kleinian Singularities, Duke 92 (1998), 605--635.
[CB1] W. Crawley-Boevey, Preprojective algebras, differential operators
and a Conze embedding for deformations of Kleinian singularities,
Comment. Math. Helv. 74 (1999), 548-574.
[CB2] W. Crawley-Boevey, Geometry of the Moment Map for Representations of Quivers, Compositio Mathematica 126 (2001), 257--293.
[CB3] W. Crawley-Boevey, Decomposition of Marsden-Weinstein Reductions
for Representations of Quivers, Compositio Mathematica 130 (2002),
225--239.
[CB4] W. Crawley-Boevey, Normality of Marsden-Weinstein reductions for
representations of quivers, Math. Ann. 325 (2003), 55--79.
[DR1] V. Dlab and C.M. Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc. 6 (1976), no. 173.
[DR2] V. Dlab and C.M. Ringel, Eigenvalues of Coxeter transformations
and the Gelfand-Kirillov dimension of the preprojective
algebras, Proc. Amer. Math. Soc. 83 (1981), 228--232.
[DR3] V. Dlab and C.M. Ringel, The module theoretical approach to
quasi-hereditary algebras, in: Representations of Algebras and Related
Topics, Kyoto, 1990, Cambridge Univ. Press, Cambridge,
1992, pp. 200--224.
[GL] W. Geigle and H. Lenzing, Perpendicular categories with
applications to representations and sheaves. J. Algebra 144 (1991),
273--343.
[GLS1] C. Geiss, B. Leclerc and J. Schroer, Semicanonical bases and
preprojective algebras, Ann. Scient. Norm. Sup. 38 (2005),
193--253.
[GLS2] C. Geiss, B. Leclerc and J. Schroer, Rigid modules over preprojective algebras, Invent. math. 165 (2006), 589-632.
[GLS3] C. Geiss, B. Leclerc and J. Schroer, Semicanonical bases and
preprojective algebras II: a multiplication formula, Compositio Math.
143 (2007), 1313--1334.
[GLS4] C. Geiss, B. Leclerc and J. Schroer, Kac-Moody groups and cluster algebras, Adv. Math. 228 (2011), 329--433.
[GS] C. Geiss and J. Schroer, Extension-orthogonal components of
preprojective varieties, Trans. Amer. Math. Soc. 357 (2004), 1953--1962.
[KS] M. Kashiwara and Y. Saito, Geometric construction of crystal bases, Duke Math. J. 89
(1997), 9--36.
[K] H. Krause, Representations of quivers via reflection functors, arXiv:0804.1428v2.
[L] H. Lenzing, Wild canonical algebras and rings of automorphic forms.
Finite-dimensional algebras and related topics (Ottawa, ON, 1992),
191-212, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 424 (Kluwer
Acad. Publ., Dordrecht, 1994).
[Lus1] G. Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4 (1991), 365--421.
[Lus2] G. Lusztig, Affine quivers and canonical bases, Inst. Hautes studes Sci. Publ. Math. No. 76 (1992), 111--163.
[MR] J. McConnell and C. Robson, Noncommutative Noetherian rings, GSM 30, (Amer. Math. Soc., Providence, RI, 2000).
[R-VdB] I. Reiten and M. Van den Bergh, Two-dimensional tame and
maximal orders of finite representation type, Mem. Amer. Math. Soc. 80
(Amer. Math. Soc., Providence, 1989), no. 408.
[R1] C.M. Ringel, The preprojective algebra of a quiver, Algebras and
modules, II (Geiranger, 1996), 467--480, CMS Conf. Proc. 24 (Amer.
Math. Soc., Providence, RI, 1998).
[R2] C.M. Ringel, The preprojective algebra of a tame quiver: the
irreducible components of the module varieties. Trends in the
representation theory of finite-dimensional algebras (Seattle, WA,
1997), 293--306, Contemp. Math. 229 (Amer. Math. Soc., Providence, RI,
1998).
