# Groupes discrets et algèbres des opérateurs

Tous les résumés
Taille : 98 kb
Organisateurs :
• Guillermo Cortiñas (University of Buenos Aires)
• Andrés Navas Flores (University of Santiago de Chile)
• Mikael Pichot, (McGill University)
• Guoliang Yu (Texas A&M University)
• Andres Navas
Universidad de Santiago de Chile (USACH)
On the affine isometric actions over a dynamics.
Résumé en PDF
Taille : 37 kb
We will review some results concerning fixed points for twisted affine actions on Banach spaces for which there is a bounded orbit. We will first remind that the twisting comes from an abstract dynamics, and the existence of a fixed point in the right space is sometimes related to the dynamics of this action.
• Bogdan Nica
McGill University and Texas A&M
C*-algebras of hyperbolic groups - To infinity and back
Résumé en PDF
Taille : 37 kb
I will discuss the (somewhat surprising) role played by the boundary in studying the reduced C*-algebra of a hyperbolic group.
• Rufus Willett
University of Hawaii
K-homology and localization algebras
Résumé en PDF
Taille : 38 kb
I'll discuss a new model for K-homology based on a non-commutative generalization of the localization algebra of Guoliang Yu. I'll then talk about how this model gives rise to a 'controlled' picture of K-homology, and some applications to computing the K-theory and K-homology of crossed product C*-algebras associated to actions of discrete groups on compact spaces, among other things. This is based on joint work with Marius Dadarlat and Jianchao Wu, and with Guoliang Yu.
• Rodolfo Viera
Universidad de Santiago de Chile (USACH)
Densitites non-realizable as the Jacobian of a 2-dimensional bi-Lipschitz map are generic
Résumé en PDF
Taille : 38 kb
In this talk, positive functions defined on the plane are considered from a generic viewpoint, both in the continuous and the bounded setting. By pursuing on constructions of Burago-Kleiner and McMullen, we show that, generically, such a function cannot be written as the Jacobian of a bi-Lipschitz homeomorphism.
• Gisela Tartaglia
The Farrell-Jones conjecture for Haagerup groups and $\mathcal{K}$-stable coefficients.
Résumé en PDF
Taille : 84 kb
A celebrated theorem of Higson and Kasparov says that if $G$ is Haagerup group then the topological $K$-theory assembly map (the Baum-Connes assembly map) with coefficients in a $G$-$C^*$-algebra $A$ $H_*^G(\underline{EG},K^{\mathrm{top}}(A))\to K_*^{\mathrm{top}}(C^*_r(G,A))$ is an isomorphism. Here $C^*_r(G,A)$ is the reduced $C^*$-algebra crossed product. Thus the Higson-Kasparov theorem establishes the Baum-Connes conjecture for Haagerup groups. In joint work with G. Cortiñas we have shown that if $G$ is Haagerup, $\mathcal{K}$ is the ideal of compact operators, $I$ is a $K$-excisive ring, $A$ a $G$-$C^*$-algebra and $B=I\otimes_{\mathbb Z}(A\otimes_{\mathrm{min}}\mathcal{K})$ then the algebraic $K$-theory assembly map (the Farrell-Jones assembly map) $H_*^G(\underline{EG}, K(B))\to K_*(B\rtimes G)$ is an isomorphism. Here $\rtimes$ is the algebraic crossed product. Thus the latter result establishes Farell-Jones conjecture with $\mathcal{K}$-stable coefficients. The talk will review this result and report on our current project with Cortiñas and Willett to partly extend this to rings of coefficients which are stable under the ideal of trace-class operators.
• Mitsuru Wilson
In this talk, I will discuss a construction of pseudo-differential for a noncommutative analogue $SU(3)_\theta$ of the special unitary group $SU(3)$ viewed as a quantum group. In geometry, pseudo-differential calculus is a global concept that is used to reveal the global geometry. The constructions very much carry over to the $C^*$-algebra and quantum group settings. This work is based on a collaboration with a Ph.D. student Carlos Rodriguez.