Milen YAKIMOV (Lousiana State),
Multiparameter quantum algebras.
[Multiparameter twists of quantum groups and quantum Schubert cell algebras were considered by many authors after the work of Artin, Shelter and Tate. We will prove a conjecture of Brown and Goodearl that the prime ideals of the first class of algebras are completely prime. For the second class of algebras we will prove a conjecture of Goodearl and Lenagan that their H-primes are polynormal, compute the dimensions of the Goodearl-Letzter strata of their spectra, and prove that they are catenary.]
Lundi 23 janvier 2012 à 14h00
Frédéric CHAPOTON (Lyon 1),
Triangulations de plans projectifs et séries d'algèbres de Lie.
[Alors qu'on connait des triangulations minimales des plans projectifs sur ℝ et sur ℂ, on dispose seulement d'un candidat pour le plan projectif sur les quaternions, et le cas des octonions reste ouvert. Il semble que la théorie des représentations des algèbres de Lie puisse apporter un éclairage nouveau à ce problème.]
Lundi 30 janvier 2012 à 14h00
Tom SUTHERLAND (Oxford),
Stability conditions for Painlevé quivers.
[To each of the Painlevé equations we associate a quiver drawn on the Riemann sphere by considering trajectories of a one-dimensional family of quadratic differentials with prescribed poles. These quadratic differentials parameterise the base of a Hitchin integrable system whose isomonodromic deformations are described by the solutions of the corresponding Painlevé equation. We will describe a connected component of the space of numerical stability conditions of the Ginzburg algebra of these quivers via the periods of the Seiberg-Witten differential on the spectral elliptic curves.]
Lundi 6 février 2012 à 14h00
Fernanda PEREIRA (IMJ et Paris 7),
Minimal Affinizations of Quantum Groups.
[The concept of minimal affinization, introduced by V. Chari, arose from the impossibility of extending, in general, a representation of the quantum group associated to a simple Lie algebra to the quantum group associated to its loop algebra, which is always possible on the classical context. The classification of the equivalence classes of minimal affinizations is complete when the Lie algebra involved is not of the type D or E, and in type D or E it is done for some cases of highest weight. We present some partial results in the direction of finishing this classification.]
Lundi 13 février 2012 à 14h00
Pierre BAUMANN (Strasbourg),
Polytopes de Mirković-Vilonen affines (travail en commun avec J. Kamnitzer et P. Tingley).
Lundi 20 février 2012 à 14h00
Gleb KOSHEVOY (Moscow),
Toric varieties and cluster algebras.
[To a framed acyclic quiver, we associate a smooth toric variety.
To a cluster algebra of SLn/N, we associate a toric variety (smooth for n≤ 5).
We will also discuss relations between these two constructions of toric varieties.]