-
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 :
,
,
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).