Programme of the Conference

The meeting will start on June 9 at 11:00 and end on June 10 at 17:00. The talks are 50 minutes long and the minicourse lectures are 60min long. All of them will take place in Room S3 124 or 122 on Campus 2. We will have lunch at the self-service restaurant of the campus. There will be a conference dinner on Thursday evening. Here is the detailed programme:

• J. Bichon (Clermont-Ferrand) Graded twisting of quantum groups I will present the construction of graded twisting of quantum groups, and some of its applications. The talk will be based on joint work with Sergey Neshveyev and Makoto Yamashita.
• M. Brannan (Texas A&M) Integration over compact quantum groups These lectures will be centered around the problem of computing (or approximating) integrals of polynomial functions over a compact quantum group with respect to the Haar state. Topics to be covered will include: some basic facts about compact quantum groups and their Haar states, the Weingarten calculus for free quantum groups and some applications to free probability, hyperlinear Haar traces, amenable Haar traces, and some applications to the structure of exotic quantum group C*-algebras.
• K. De Commer (Vrije Universiteit Brussel) Torsion-freeness for fusion rings Torsion-freeness for discrete quantum groups was defined by R. Meyer in order to formulate a Baum-Connes conjecture in the setting of discrete quantum groups. In this talk, we define torsion-freeness for abstract rigid tensor C*-categories and abstract fusion rings. We discuss several stability results for torsion-freeness, and show in particular that the tensor C*-categories associated with the free unitary quantum groups of Wang and Van Daele are torsion-free. This is joint work with Y. Arano.
• P. Fima (Paris) K-amenability for amalgamated free product of K-amenable discrete quantum group We explain how to prove K-amenability for amalgamated free product of K-amenable discrete quantum groups and how to compute KK-theory of amalgamated free product of general C*-algebras.
• U. Franz (Besançon) What is the Laplacian of the free sphere?
• A. Freslon (Orsay) The von Neumann algebras of free orthogonal quantum groups Free orthogonal quantum groups are a toy model for adapting ideas from geometric group theory to the quantum setting. This has in particular led to several important results on the structure of the associated von Neumann algebras. One aspect which has not attracted so much attention yet is maximal abelian subalgebras (MASAs for short). There are plenty of such subalgebras and the works of Isono and Fima-Vergnioux ensure that they can never be regular. It is therefore natural to look for singular examples. The case of free groups suggests two candidates : the radial and generator MASAs. I will present a recent work with R. Vergnioux proving that the radial MASA is singular (and even strongly mixing). The proof involves a detailed analysis of the Jones-Wenzl recursion relations and some technical estimates in the representation category of free quantum orthogonal groups.
• P. Tarrago (Tours) Free wreath product and planar algebras In this talk, I will give a description of the intertwiner spaces of the free wreath product of a matrix compact quantum group with a noncommutative permutation group. This description, which is based on the construction of a free product of planar algebras, yields an explicit basis of the intertwiner spaces. At the end of the talk, I will discuss some applications to the law of characters and the representation theory of the free wreath product. This is a joint work with Jonas Wahl.
• M. Ulrich (Besançon) Elucidating Dual Groups The goal of my talk will be to introduce the concept of a dual group and to give some new results about their structure.

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