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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.
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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.
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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.
|
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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 :
, ,
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).