Programme

Plenary Lectures

• Erik Guentner: Decomposition complexity of metric spaces

• Nigel Higson: Analytic properties of groups and K-theory conjectures

• Wolfgang Lück: On the Borel Conjecture and related topics  [slides]

  The Borel Conjecture predicts for two closed aspherical manifolds M and N that they are homeomorphic if and only if their fundamental groups agree and that in this case every homotopy equivalence is homotopic to a homeomorphism. This may be viewed as the topological version of Mostow rigidity. It is related to the Farrell-Jones Conjecture about the algebraic K- and L_theory of group rings and the Baum Connes Conjecture about the topological K-theory of reduced group C*-algebras. We present the recent work together with Bartels, where we prove the Farrell-Jones Conjecture and hence the Borel Conjecture in dimension greater or equal to 5 for a large class of groups which includes word-hyperbolic groups and CAT(0)-groups and is closed under directed colimits , taking subgroups and direct products. This implies that these conjectures are true for certain interesting groups (Tarsky monsters, groups with expanders, limit groups) and those exotic aspherical manifolds constructed by Mike Davis.

• Narutaka Ozawa: Recent advances in classification of finite von Neumann algebras  [slides]

• Marc Sapir: TBA

• Alain Valette: Stability properties of the class of Haagerup groups

  A group has the Haagerup property, or is a-T-menable, if it admits a metrically proper, isometric action on a Hilbert space. By a celebrated result of Higson-Kasparov, groups with the Haagerup property satisfy the Baum-Connes conjecture with coefficients. The class of Haagerup groups is closed under direct and free products, but not under arbitrary semi-direct products. We exhibit a class of semi-direct products for which the Haagerup property is preserved; in particular we show that the Haagerup property is stable under wreath products. This is joint work with Y. de Cornulier and Y. Stalder.

Introductory courses for PhD students

• Erik Guentner: Permanence in coarse geometry

• Nigel Higson: Analytic properties of groups and K-theory conjectures, Intoduction

  This lecture is an introduction to the subject-matter of the plenary talk by the same speaker.

Contributed talks

• Goulnara Arzhantseva: Compression of uniform embeddings of groups into Hilbert and Banach spaces

• Cornelia Drutu: Median spaces and properties (T) and Haagerup. Mapping class groups.

  Median spaces are non-discrete generalisations of CAT(0) cubical complexes. Properties (T) and Haagerup can be characterised in terms of actions on median spaces. We will explain why the asymptotic cones of mapping class groups are median, and how can this be used to study their subgroups. The first part of the talk is on joint work with I. Chatterji and F. Haglund, the second on joint work with J. Behrstock and M. Sapir.

• Ian Hambleton: Assembly maps and controlled topology

  The Farrell-Jones and Baum-Connes assembly maps have a unified description in terms of equivariant controlled topology, and this point of view has been very useful in recent progress in understanding assembly for new classes of infinite discrete groups, at least for algebraic K-theory and L-theory. In the talk I will describe some aspects of this theory, and its application to studying assembly maps for group extensions. This is based on joint work with Erik Pedersen and David Rosenthal.

• Pierre de la Harpe: Degrees of irreducible representations of wreath products with finite groups

  (Joint work with L. Bartholdi)

• Ashot Minasyan: Infinite groups with fixed point properties  [slides]

  (Joint work with G. Arzhantseva, M.R. Bridson, T. Januszkiewicz, I.J. Leary and J. Swiatkowski)
  We construct finitely generated groups with strong fixed point properties. Let X_ac be the class of Hausdorff spaces of finite covering dimension which are mod-p acyclic for at least one prime p. We produce the first examples of infinite finitely generated groups Q with the property that for any action of Q on any space X_ac, there is a global fixed point. Moreover, Q may be chosen to be simple and to have Kazhdan's property (T).
  We also construct a finitely presented infinite group P that admits no non-trivial action by diffeomorphisms on any smooth manifold from X_ac.

• Nicolas Monod: Some properties of CAT(0) groups

  (Joint work with P.-E. Caprace.)

• Yves Stalder: Fixed point properties and ultralimits, after Gromov  [slides]