Unité Mixte de Recherche CNRS 5582 Université Grenoble I
UFR de Mathématiques
Institut Fourier 100 rue des maths, BP 74, 38402 St Martin d'Hères cedex, (France)
Téléphone : (+33/0) 4.76.51.46.56 Fax : (+33/0) 4.76.51.44.78
Téléphone : (+33/0) 4.76.51.46.56 Fax : (+33/0) 4.76.51.44.78
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2008 Summer School
The 2008 Summer school takes place at the Institut Fourier from June 16th to July 4th, 2008.
The theme of the 2008 school is the theory of quiver representations, in its algebraic and geometric aspects. In this subject, there have been important advances during the last twenty-five years (work of Lusztig, Nakajima, King, Crawley-Boevey...), in relation to algebraic geometry (McKay correspondence, punctual Hilbert schemes, geometric invariant theory) and to other domains of representation theory (quantum groups, canonical bases).
The school will aim at presenting an overview of the subject, with its algebraic aspects (which only require small prerequisites of representation theory), and its more advanced geometric aspects. The latter play a very important role in recent developments.
The first two weeks will be devoted to fundamental courses aimed at pre-graduate and graduate students ; these courses will present the basic notions of the domain, and the main directions of research. The third week will consist of seminar talks on the latest developments.
List of confirmed speakers :
K. BAUR (Zurich)
J. BERTIN (Grenoble)
G. BOBINSKI (Torun)
S. BOISSIERE (Nice)
A. BORALEVI (Florence)
M. BRION (Grenoble)
L. EVAIN (Angers)
V. GINZBURG (Chicago)
G. GONZALEZ-SPRINBERG (Grenoble)
I. GORDON (Edinburgh)
J.C. JANTZEN (Aarhus)
D. JUTEAU (Paris VII)
V. LAKSHMIBAI (Boston)
B. LECLERC (Caen)
S. LOKTEV (Moscow)
I. LOSEU (MIT)
V. MEHTA (TIFR, Mumbai)
M. PERLING (Bochum)
K.N. RAGHAVAN (Chennai)
O. SCHIFFMANN (Paris)
O. SERMAN (Nice)
D. SHMELKIN (Moscou)
C. SORGER (Nantes)
F. VACCARINO (Turin)
G. WILLIAMSON (Freiburg)
List of confirmed courses :
First week (June 16th - 20th) :
Quiver representations (Brion)
Punctual Hilbert schemes (Bertin)
McKay correspondence (Gonzalez-Sprinberg)
Hall algebras (Schiffmann)
Second week (June 23rd - 27th) :
Crystal bases and Fock space (Leclerc)
Haiman’s work on the n ! theorem, and beyond (Gordon)
Nakajima varieties (Ginzburg)
Moment graphs and representations (Jantzen)
Canonical bases and moduli spaces (Schiffmann)
Third week (June 30rd - July 4th) :
A series of talks will be given by the following speakers :
Geometric construction of cluster algebras and cluster categories, Karin Baur
Directing modules are regular in codimension one, Grzegorz Bobinski
The McKay correspondence for polyhedral singularities, S. Boissière
Quivers and homogeneous vector bundles on flag manifolds, Ada Boralevi
Cohomology ring of punctual Hilbert Schemes, Laurent Evain
Symplectic reflection algebras, Victor Ginzburg
Intersection cohomology in positive characteristic I, Daniel Juteau
Affine Grassmannians and their Schubert varieties, V. Lakshmibai
Spherical symplectic reflection algebras via quantum Hamiltonian reduction, Sergey Loktev
Quantized symplectic actions and W-algebras, Ivan Losev
The strong Harder-Narasimhan filtration for G-bundles (joint work with Trivedi and Subramanian), Vikram Mehta
The derived category of coherent sheaves on a toric surface (joint work with L. Hille), Markus Perling
Initial ideals of tangent cones to Schubert varieties in orthogonal Grassmannians, K. N. Raghavan
Orthogonal bundles on curves and quiver representations, Olivier Serman
Geometric methods for semi-invariants of quivers:from theorems to software, Dmitri Shmelkin
A symplectic resolution for the binary tetrahedral group, Christoph Sorger
An Hilbert to Chow morphism for the non-commutative Hilbert scheme and moduli spaces of linear representations, Francesco Vaccarino
Intersection cohomology in positive characteristic I and II, Geordie Williamson
We would like to thank these organizations for their financial support :
Université Joseph Fourier
CNRS
Ministry of Foreign Affairs
Région Rhone-Alpes