J. Bichon: Inner linear Hopf algebras. A (discrete) group is said to be linear when it has a faithful finite-dimensional linear representation. We will discuss the Hopf algebraic analogue of this classical notion. The talk is based on joint work with Teodor Banica.

B. Collins: Connes embedding property for A_o(n) and A_s(n). We discuss the Connes embedding property for the quantum groups A_o(n) and A_s(n).

U. Franz: Characterisations of idempotent states on finite and compact quantum groups. The idempotent measures on a locally compact group G are all given by Haar measures of compact subgroups of G. Since Pal's example (1996) we know that the analogous statement is false for quantum groups. Im my talk I will present new examples of idempotent states on finite and compact quantum groups that are not induced by Haar states of compact quantum subgroups. Furthermore I will present several characterisations of idempotent states on finite and compact subgroups, e.g. in terms of group-like projections, quantum subhypergroups, and (expected) coidalgebras.

E. Germain: Injective envelope and Martin boundary for some reduced group C*-algebras. We prove that, for any discrete group, the cross product of the set of extremal points in a Martin boundary of the group by that group is contained in the injective envelope of the reduced group $C^*$-algebra as soon as the extremal points are a closed set, thus extending a result of Ozawa for the free group.

D. Goswami: Quantum isometry groups. We present an overview of quantum isometry groups in the framework of both classical and noncommutative geometry. We shall discuss the main ideas of definition and existence of such quantum groups, and also some interesting examples and applications. In particular, we shall show how many well-known quantum groups including $SO_q(3)$ and the free and half-liberated orthogonal quantum group, can be identified as quantum isometry groups of some suitable spectral data. The talk is based on joint work with J. Bhowmick, T. Banica and A. Skalski.

P. Guillot: Cohomology of twists on group algebras. (joint with C. Kassel) We show how to compute a certain group of equivalence classes of invariant Drinfeld twists on the algebra of a finite group G over a field k of characteristic zero. This group is naturally isomorphic to the second lazy cohomology group of the Hopf algebra of k-valued functions on G, which has received attention lately. We give a general method, showing in particular that this group is finite when k is algebraically closed, and may be non-abelian.

G. Halbout: Deformation of linear Poisson orbifold. This is a joined work with J.-M. Oudom and X. Tang. Let Gamma be a finite group acting faithfully and linearly on a vector space V. Let T(V) (S(V)) be the tensor (symmetric) algebra associated to V which has a natural Gamma action. We study generalized quadratic relations on the tensor algebra T(V) Gamma. We prove that the quotient algebras of T(V) Gamma by such relations satisfy PBW property. Such a quotient algebra can be viewed as a quantization of a linear or constant Poisson structure on S(V) Gamma, and is a natural generalization of symplectic reflection algebra. I will also discuss globalization of such results on general orbifold.

I. Heckenberger: Nichols algebras and Weyl groupoids. This is a joint work with H.-J. Schneider. For the definition of quantized enveloping algebras there exist well-developed universal constructions. In Lusztig's approach one starts with a finite-dimensional graded module over the group algebra of $Z^n$ with additional properties, which determines uniquely the upper triangular part of the quantized enveloping algebra via a non-degenerate bilinear form. (The quantized enveloping algebra is then essentially the Drinfeld double of this algebra.) An abstract Hopf algebraic viewpoint allows a significant generalization of this construction called Nichols algebra. An interesting question is, how Nichols algebras look like for more general graded modules over more general group algebras (or even Hopf algebras), for example if there is always a PBW basis or if one can calculate the dimensions of homogeneous components. Towards this, root systems and their symmetries (Weyl groupoids) are attached to any Yetter-Drinfeld module over a Hopf algebra satisfying a certain semisimplicity assumption. The obtained combinatorics generalizes ordinary root systems and their Weyl group symmetry, and can be used to find new Hopf algebras efficiently and to achieve essential progress in the classification of finite-dimensional pointed Hopf algebras.

C. Kassel: Colloquium talk: Identites polynomiales. Si X,Y,Z sont des matrices carrees de taille 2, on a (XY-YX)^2Z-Z(XY-YX)^2=0. C'est un exemple simple, mais non trivial de ce qu'on appelle une identité polynomiale ; cet exemple est apparu en 1937 dans un article de W. Wagner sur les fondements de la géométrie projective. Existe-il d'autres identités du même type pour les matrices ? Comment en trouver ? A quoi servent-elles ? Voilà quelques questions auxquelles je répondrai dans mon exposé. En passant, je montrerai aussi comment munir une algèbre de matrices d'une graduation indexée par un groupe quelconque.

C. Kassel: Homology (of) Hopf algebras. (Joint work with J. Bichon.) To any Hopf algebra H we associate two commutative Hopf algebras, which we call the first and second lazy homology Hopf algebras of H. These algebras are related to the lazy cohomology groups based on the so-called lazy cocycles of H by universal coefficient theorems. When H is a group algebra, then its lazy homology can be expressed in terms of the 1- and 2-homology of the group. When H is a cosemisimple Hopf algebra over an algebraically closed field of characteristic zero, then its first lazy homology is the Hopf algebra of the universal abelian grading group of the category of corepresentations of H. We also compute the lazy homology of the Sweedler algebra.

S. Natale: Hopf algebra extensions of group algebras and Tambara-Yamagami categories. An important problem related to the classification of semisimple Hopf algebras was the question of deciding the existence of examples which were not group-theoretical. Recently, this question has been answered by Nikshych, who constructed a family of semisimple Hopf algebras which are not group-theoretical as an extension of the algebra of functions on the group Z_2 by a twisted group algebra. In this talk we shall consider Hopf algebra extensions of a triangular semisimple Hopf algebra A by the group Z_2, which are in a sense dual to those mentioned before. We describe the (co-)representation theory of such Hopf algebras, which generalizes at the Hopf algebra level, the so-called Tambara-Yamagami categories. We relate the construction to the notion of G-equivariantization of fusion categories. Finally, we show how the structure of such Hopf algebra is determined by certain group-theoretical data.

S. Vaes: Von Neumann algebras and measure preserving actions of countable groups. Using a construction of Murray and von Neumann (1943), countable groups and their actions on measure spaces give rise to algebras of Hilbert space operators, called von Neumann algebras. The aim of the talk is to discuss the highly subtle relation between a group action and its von Neumann algebra: Connes' 1976 theorem says that all amenable group actions essentially lead to one single von Neumann algebra, while Popa's recent rigidity results provide group actions whose von Neumann algebra entirely remembers the group and the action.

N. Vander Vennet: Boundaries of universal quantum groups. We describe how to attach a topological boundary to universal discrete quantum groups in the same spirit as can be done for free groups. We explain the link with exactness and solidity and give a probabilistic interpretaion of the boundary.

R. Vergnioux: New examples of fusion rules for quantum groups. I will describe the fusion rules for two recently introduced families of compact quantum groups: the (duals of) quantum reflection groups, which have exponential growth, and the half-liberated orthogonal groups, which have polynomial growth.

C. Voigt: Baum-Connes conjecture and quantum groups. The Baum-Connes conjecture predicts the K-theory of group $C^*$-algebras. We will first review some facts about this conjecture and then explain how to extend it to a certain class of quantum groups. Concretely we will discuss the dual of quantum SU(2) and free orthogonal quantum groups.