Departement de Mathematique d'Orsay

(english version)


Les 20 et 21 Décembre 2007.

- Lieu : Tous les exposés auront lieu au
Petit Amphi., Bâtiment 425, Université de Paris-Sud Orsay, 15 rue G. Clemenceau, 91400 ORSAY

Pour s'y rendre, lire cette page.

- Orateurs :

Goulnara Arzhantseva (Université de Genève).
Brian Bowditch (Université de Warwick).
Misha Gromov (IHES).
Jon McCammond (Université de Californie à Santa Barbara).
Nicolas Monod (Université de Genève).
Panos Papasoglu (Université d'Athènes).
Alain Valette (Université de Neuchâtel).
Richard Weidmann (Université Heriot-Watt d'Edimbourg).
Dani Wise  (Université McGill de Montréal).

Graham Niblo, qui devait faire un exposé, est tombé malade ; nous lui souhaitons un prompt rétablissement.

- Programme :

Jeudi 20 Décembre Vendredi 21 Décembre
09h00-09h30 : accueil des participants, café. 09h00-09h50 : Gromov's theorem on polynomial growth, after Bruce Kleiner - A. Valette.                             
09h30-10h20 : Product groups acting on manifolds - N. Monod. 10h00-10h30 : pause café.
10h30-11h20 : Special cube complexes (I) - D. Wise. 10h40-11h30 : From Combinatorics to Topology via Algebraic Isoperimetry - M. Gromov.
11h30-13h00 : déjeuner. 11h30-12h20 : Maps onto hyperbolic groups - R. Weidmann.
13h00-13h50 : Higher isoperimetric inequalities for complexes and groups - P. Papasoglu. 12h30-14h00 : déjeuner.
14h00-14h50 : Pulling apart orthogonal groups to find continuous braids - J. McCammond. 14h00-14h50 : Random groups and uniform embeddings into Hilbert space - G. Arzhantseva.
15h00-15h30 : pause café. 15h00-15h50 : Special cube complexes (II) - D. Wise.
15h30-16h20 : One-ended subgroups of the mapping class group - B. Bowditch. 16h00-... : café.

- Résumés :

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

Résumé :
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.

Résumé :
A subgroup of the mapping class group of a compact surface is "purely pseudoanosov" if every non-trivial element is pseudoanosov. It can be shown that, up to conjugacy, there are only finitely many purely pseudonanosov copies of a given finitely presented one-ended group in any given mapping class group. It is unknown whether such a subgroup can exist at all. We shall give an outline of the proof, focusing on the case of surface subgroups. In this case, one deduces that all but finitely many surface-by-surface groups of given genera contain a free abelian subgroup of rank 2.  The argument uses ideas from the proof of the Ending Lamination Conjecture by Minsky, Brock and Canary.

M. Gromov.  From Combinatorics to Topology via Algebraic Isoperimetry.

N. Monod.  Product groups acting on manifolds.

Résumé :
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.

Résumé :
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).

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

Résumé :
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.

Résumé :
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.  Maps onto hyperbolic groups.

Résumé :
Sela gives a complete description of Hom(H,G) where G is an arbitrary finitely presented group and H is a torsion-free hyperbolic group. Despite this fact it is known that there is no uniform algorithm that decides whether Hom(H,G) contains an epimorphism. We discuss classes of hyperbolic groups where epimorphisms can be effectively described.

D. Wise.  Special cube complexes.

Résumé :
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.

- Aide aux doctorants :

Nous pouvons financer une dizaine de doctorants pour  un montant de 100€ par personne. Pour les détails, nous contacter.

Attention ! Date limite pour déposer une demande : vendredi 23 Novembre 2007.

- Organisateurs :  Frédéric Haglund, Pierre Pansu.

Contacts : secretariat (point) topologie (à) math (point) u-psud (point) fr , frederic (point) haglund (à) math (point) u-psud (point) fr

- Soutien financier :

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