## Séminaire d’Algèbres d’Opérateurs

### jeudi 15 juin 2017 à 14:00 : Salle 2015 - Sopbie Germain Place Aurélie Nemours, Campus des Grands Moulins-UP7D

Suivant les travaux de Chabert, Echterhoff et Oyono-Oyono, nous présenterons un principe de restriction adapté au cas des groupoïdes étales. Nous expliquerons comment utiliser ce principe pour prouver que les produits croisés de C*-algèbres par des actions d’une certaine classe de groupoïdes vérifient la formule de Künneth en K-théorie quantitative (et donc en K-théorie).

### jeudi 18 mai 2017 à 14:00 : Salle 2015 - Sopbie Germain Place Aurélie Nemours, Campus des Grands Moulins-UP7D

In this talk I will present joint work with Andreas Thom on bounded normal generation (BNG) for projective unitary groups of von Neumann algebras. We say that a group has (BNG) if the conjugacy class of every nontrivial element and of its inverse generate the whole group in finitely many steps. After explaining how one can prove (BNG) for the projective unitary group of a finite factor, I plan to present applications to automatic continuity of homomorphisms.
If time permits I will close the talk with recent results on uncountable cofinality and the Bergman property for unitary groups of von Neumann algebras.

### jeudi 27 avril 2017 à 14:00 : Sophie Germain - 2015 Place Aurélie Nemours, Campus des Grands Moulins-UP7D

Cet exposé présente des résultats obtenus en collaboration avec M.Weber. Toute représentation de dimension finie d d’un groupe quantique compact induit une action sur l’algèbre de Cuntz O(d.) Nous combinons des résultats de classifications des groupes quantiques compacts de partition avec la théorie de Kirchberg-Phillips pour identifier l’algèbre des points fixes grâce à sa K-théorie.

### jeudi 20 avril 2017 à 14:00 : Salle 2015 - Sopbie Germain Campus des Grands Moulins

In recent years, the polynomial method has proven a powerful tool in different areas of mathematics, including number theory, harmonic analysis, computer science and combinatorics. We will discuss some improvements of this method over Euclidean space, including a sharp polynomial partitioning theorem over arbitrary varieties and new estimates on the behaviour of the connected components of real algebraic sets. As an application of these results, we provide a general degree-sensitive incidence bound for families of algebraic varieties of arbitrary degree and dimension.

### jeudi 23 mars 2017 à 11:00 : Salle 2015 - Sophie Germain Campus des Grands Moulins

We give an introduction to the Farrell-Jones Conjecture which aims at the algebraic K- and L-theory of group rings. It is analogous to the Baum-Connes Conjecture about the topological K-theory of reduced group C^*-algebras. We report on the substantial progress about the Farrell-Jones Conjecture which was made in the last years, it is meanwhile known for
hyperbolic groups, CAT(0)-groups, S-arithmetic groups and lattices in almost connected Lie groups. We give a survey on its applications, for instance to the Novikov Conjecture, the Borel Conjecture and the classification of hyperbolic groups with a sphere of dimension greater or equal to five as boundary.

### jeudi 9 février 2017 à 11:00 : Salle 2015 - Sophie Germain Campus des Grands Moulins

We compare different constructions of cyclic cocycles for the algebra of complete symbols of pseudodifferential operators and show that our comparison result leads to interesting index-theoretic consequences and a construction of invariants of the algebraic K-theory of the algebra of pseudodifferential symbols. This is a joint work with H. Moscovici.

### jeudi 12 janvier 2017 à 11:00 : Salle 2015 - Sophie Germain Campus des Grands Moulins

I will give an overview over the state of the classification programme for separable, simple, nuclear C*-algebras. The Universal Coefficient Theorem remains a crucial but mysterious ingredient, both for classification and for structural results such as quasidiagonality ; I will outline how the UCT comes in and speculate about possible strategies to approach the UCT problem.

### jeudi 29 septembre 2016 à 14:00 : Salle 2015 - Sophie Germain Campus des Grands Moulins - UP7D

I will demonstrate that the free product construction for subfactors due to Bisch and Jones and its formulation for planar algebras can be used to give a systematic description of the free wreath product operation for compact quantum groups. In order to do, I will recall Jones’s notion of graph planar algebra and I will show that any subfactor planar subalgebra of the graph planar algebra of a graph with one even vertex arises as the fixed point algebra of an action of a compact quantum group on the algebra of loops of length 2 on the graph. In addition, an application to (central) approximation properties of free wreath products is given. This is joint work with Pierre Tarrago.

### jeudi 8 septembre 2016 à 15:30 : Salle 1016 - Sopbie Germain Campus Grands Moulins UP7D

The classic Birkhoff-von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this talk, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we replace a doubly stochastic matrix with a collection of measure preserving partial isomorphisms, of the unit interval, with similar properties. We show that a weaker version of this theorem still holds. Joint work with Florin Radulescu.