(version française)

DEUX JOURNÉES DE
THÉORIE GÉOMÉTRIQUE DES GROUPES
À ORSAY


Thursday December 20, Friday December 21, 2007.



- Place : All lectures will be given at
 
Petit Amphi., Bâtiment 425, Université de Paris-Sud Orsay, 15 rue G. Clemenceau, 91400 ORSAY
.

To get there see this page.


- Speakers :

Goulnara Arzhantseva (Université de Genève).
Brian Bowditch (University of Warwick).
Misha Gromov (IHES).
Jon McCammond (UC Santa Barbara).
Nicolas Monod (Université de Genève).
Graham Niblo (University of Southampton).
Panos Papasoglu (University of Athens).
Alain Valette (Université de Neuchâtel).
Richard Weidmann (Heriot-Watt University of Edinburgh).
Dani Wise  (McGill University of Montréal).


- Schedule :



Thursday December 20
Friday December 21
09h00-09h30 : Reception of participants, coffee. 09h00-09h50 : Talk 6.                                        
09h30-10h20 : Talk 1. 10h00-10h30 : Coffee.
10h30-11h20 : Talk 2. 10h40-11h30 : Talk 7.
11h30-13h00 : Lunch. 11h30-12h20 : Talk 8.
13h00-13h50 : Talk 3. 12h30-14h00 : Lunch.
14h00-14h50 : Talk 4. 14h00-14h50 : Talk 9.
15h00-15h30 : Coffee. 15h00-15h50 : Talk 10.
15h30-16h20 : Talk 5. 16h00-... : Coffee.





- Abstracts :



G. Arzhantseva.  Random groups and uniform embeddings into Hilbert space.

Abstract :
A random group is a generic representative of a given class of groups. Studying such groups gives a vision on groups in general, which has lead to spectacular applications (e.g. Gromov's construction of groups with no uniform embedding into a Hilbert space).
We focus on a new invariant R(G) with values in [0; 1], called Hilbert space compression. It describes how close any uniform embedding of the group into a Hilbert space can be to a quasi-isometry. Using infinite families of expanders, we construct (explicitly) groups which are uniformly embeddable into Hilbert space but, like Gromov's group, have zero Hilbert space compression.

This is a joint work with Cornelia Drutu and Mark Sapir.


B. Bowditch.  One-ended subgroups of the mapping class group.


Abstract :


M. Gromov. T.b.a.

Abstract :


N. Monod.  Product groups acting on manifolds.

Abstract :
We prove an alternative for volume-preserving actions of product groups upon compact manifolds, particularly if the groups have property (T). This is joint work with Alex Furman.


J. McCammond.  Pulling apart orthogonal groups to find continuous braids.

Abstract :
Suppose you were asked to complete the following analogy - symmetric groups are to braids groups as the orthogonal groups O(n) are to (blank). In this talk I'll present one possible answer to this question. Other answers are possible since it depends on how one envisions the braid groups being constructed out of symmetric groups, but most of the standard constructions do not extend to continuous groups such as O(n). The groups I'll discuss are slightly odd in that they have a continuum of generators, a continuum of relators but nevertheless have a decidable word problem (in a suitable sense), a finite dimensional Eilenberg-Maclane space (that is not locally finite) and many other nice properties. In particular, if we view Sym(n) as the subgroup of O(n) that permutes the coordinates, then Braid(n) naturally embeds as a subgroup of the pulled apart version of O(n).


G. Niblo.  Amenability, property A and Pascal's triangle.

Abstract :
Yu's property A can be viewed as a non-equivariant version of amenability for  metric spaces which, to some extent, coarsely captures the equivariance condition from the definition for groups. Spaces with property A admit a uniform embedding into Hilbert space and therefore satisfy the Novikov conjecture, and the motivation for the definition of property A was to establish the Novikov conjecture for hyperbolic spaces and groups. In this talk we will examine the proof of property A for trees and show how to generalise it for finite dimensional CAT(0) cube complexes. The methods are entirely geometric and unlike the proof by Campbell and Niblo for co-compact CAT(0) cube complexes they do not require a condition of local finiteness. As a corollary we obtain a direct proof that if a group acts properly on such a complex then the stabilisers of points at infinity (in the combinatorial boundary) are amenable. Pascal's triangle makes a guest appearance in the proof of the main theorem.
Joint work with Brodzki, Campbell, Guentner and Wright.



P. Papasoglu.  Higher isoperimetric inequalities for complexes and groups.

Abstract :
Gromov showed that if a simplicial complex satisfies a subquadratic isoperimetric inequality then it satisfies a linear one. We show that a similar theorem holds for the 2nd isoperimetric inequality provided that the 2-cycles that maximize filling volume are spheres, or, more generally, surfaces of uniformly bounded genus.


A. Valette.  Gromov's theorem on polynomial growth, after Bruce Kleiner.

Abstract :
Kleiner recently gave a new proof of Gromov's celebrated theorem on groups with polynomial growth, based on the one hand, on ideas of Colding-Minicozzi on harmonic functions on manifolds with polynomial volume growth, on the other hand on ideas of Korevaar-Schoen on Kazhdan's property (T). We shall explain the main steps in Kleiner's proof.


R. Weidmann. T.b.a.

Abstract :


D. Wise.  Special cube complexes.

Abstract :
Frederic Haglund and I have developed a theory of "special cube complexes" that are intimately related to right-angled artin groups and appear to have a surprisingly wide scope within geometric group theory. I will discuss this theory, and a variety of results and anticipated results.


- Organizers :  Frédéric Haglund, Pierre Pansu.

Contact : secretariat (dot) topologie (at) math (dot) u-psud (dot) fr , frederic (dot) haglund (at) math (dot) u-psud (dot) fr


- Financial support :

Université Paris-Sud 11 
, Département de Mathématiques d'Orsay. ,
A.N.R. "Autour de la conjecture de Cannon" (responsible: Hervé Pajot, UJF Grenoble), GDR 3066 "Géométrie, Dynamique, Représentations des Groupes"  (responsible: Bertrand Rémy, ICJ Lyon 1).