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Intérêts.
Roughly speaking, my field of research is infinite group theory (more
pedantically, geometric group theory). I have
especially focused on aspects of group theory involving unitary
representations and isometric actions on Hilbert spaces, such as
Kazhdan's Property (T), Haagerup Property and their variants. I'm also
interested in the so-called space of (marked) finitely generated
groups, structural results about locally compact groups,
and in the asymptotic geometry of connected solvable Lie groups (Dehn
function, asymptotic cones).
Publications,
submitted papers
and
prepublications.
Large-scale
geometry
- (with Romain
Tessera) Metabelian groups with quadratic Dehn
function and Baumslag-Solitar groups (11 pages, pdf)
Note: the first
versions of this paper were untitled "Embeddings of solvable
Baumslag-Solitar
groups into
discrete groups with quadratic Dehn function"
- (with Romain
Tessera) Contracting automorphisms and
Lp-cohomology in
degree one. (27 pages, pdf, to
appear in Ark. Mat.)
-
Asymptotic cones of Lie groups and cone equivalences
. (12 pages, pdf)
-
Dimension of asymptotic cones of Lie groups
. (22 pages, pdf ); J. Topology 1(2),
343-361,
2008.
- (with Romain
Tessera) Quasi-isometrically embedded free
sub-semigroups. (9 pages, dvi
,pdf ); Geom. Topol. 12
461-473, 2008.
Hilbert spaces, Haagerup
Property, Property
T,
etc.
- (with Romain
Tessera) A characterization
of relative Kazhdan Property T
for semidirect products with
abelian
groups. (14 pages, pdf), to
appear in Ergodic Theory Dynam. Systems.
- (with Bachir
Bekka) A spectral gap property for subgroups of finite
covolume
in Lie groups. (9 pages, pdf), Colloquium Math.
118 (2010) 175-182.
- (with
Raf Cluckers, Nicolas Louvet,
Romain
Tessera, and
Alain Valette) The Howe-Moore
property for real and p-adic groups (25 pages, pdf)
- On lengths on semisimple groups. (9 pages, pdf); J. Topol. Anal.
1(2) (2009) 113-121.
- (with Yves Stalder and Alain Valette) Proper
actions of wreath products and generalizations. (28
pages, pdf)
- (with Yves Stalder and Alain Valette) Proper
actions of lamplighter groups associated with free groups. (6
pages, pdf); C.R. Acad. Sci. Paris, Ser
I
346 (2008) 173-176.
- (with Romain
Tessera and Alain Valette)
Isometric group actions on Hilbert spaces:
structure of orbits. (12 pages, dvi
,pdf ),
Canadian Math. J. 60
(2008), no. 5, 1001-1009.
- (with Romain
Tessera and Alain Valette)
Isometric group actions on Hilbert spaces:
growth of cocycles. (24 pages, dvi
,pdf ), Geom. Funct. Anal.
17 (2007), 770-792.
- (with Romain
Tessera and Alain Valette)
Isometric group actions on Banach spaces and
representations vanishing at infinity. (28 pages, pdf );
Transform. Groups 13 (2008), no. 1, 125--147.
-
Dense subgroups with Property (T) in Lie groups. (9
pages, dvi
,pdf ); Comment. Math. Helv
83(1), 55-65, 2008.
-
Relative Kazhdan Property. (36 pages, dvi
,pdf );
Ann. Sci. Ecole Norm. Sup. 39(2), 301-333, 2006.
-
Finitely presentable, non-Hopfian groups with Kazhdan's Property
and infinite outer automorphism group.(8 pages,
corrected version pdf;
erratum (2010) pdf (2010) to 2007 published version; pdf;
ArXiv); Proc.
Amer. Math. Soc. 135,
951-959, 2007.
-
Kazhdan and Haagerup Properties in algebraic groups over local
fields. (11 pages, dvi ,pdf );
ArXiv); J.
Lie Theory 16, 67-82, 2006.
-
Kazhdan property for spaces of continuous functions. (4
pages, dvi ,pdf ); Bull. Belg.
Math. Soc. 13(5), 899-902, 2007. Note:
the previous versions of this paper were untitled "Kazhdan
property for function spaces".
-
Haagerup
Property for subgroups of SL2 and residually
free
groups (2
pages, dvi ,pdf ), Bull. Belg.
Math. Soc. 13(2), 341-343, 2006.
Abstract group theory and
miscellaneous
- (with Emmanuel
Breuillard) On conjugacy
growth for solvable
groups
(6
pages, pdf, to appear in Illinois J. Math.)
- On the Cantor-Bendixson rank of metabelian groups. (20 pages,
pdf), to appear in Ann. Inst. Fourier.
- (with Luc
Guyot and
Wolfgang
Pitsch)
The
space of subgroups of an
abelian group.
(22 pages, pdf ),
J. London Math. Soc. 81(3) (2010)
727-746.
- (with Aditi Kar)
On Property
(FA) for wreath
products. (8
pages, pdf, to appear in J. Group
Theory)
- A sofic group away from amenable groups. (6 pages, pdf), to appear in Math. Ann.
-
The space of finitely generated rings. (8 pages, dvi
,pdf ), Internat. J. Algebra
Comput.
19(3) (2009) 373-382.
- Infinite conjugacy classes
in
groups acting on trees. (9 pages, dvi
,pdf ), Groups Geom. Dyn. 3(2)
(2009)
267-277.
- (with Avinoam Mann)
Some residually finite groups
satisfying laws. (5 pages, dvi
,pdf ); Geometric Group Theory, Trends in
Math. 45-50, Birkhäuser 2007.)
- (with Luc
Guyot and
Wolfgang
Pitsch)
On
the isolated points in the
space of groups. (30 pages, pdf ), J.
Algebra 307(1) (2007), 254-277.
- Strong
boundedness of Homeo(Sn). Appendix to Distortion in
transformation groups by Danny Calegari and Michael H. Friedman. (pdf);
Geom. Topol. 10 (2006), 267-293
(appendix p.290).
-
Finitely presented wreath products and double coset
decompositions.(21 pages, dvi
,pdf ); Geom. Dedicata
122 (2006), 89-108.
- (with Laurent
Bartholdi)
Infinite groups with large balls of torsion elements and
small entropy.(8
pages, dvi
,pdf );
Archiv der Mathematik 87(2),
104-112, 2006.
- (with Pierre
de la Harpe)
Décompositions de groupes par produit direct et
groupes de Coxeter. (French with English abstract, 23 pages,
en français, pdf ); Geometric Group
Theory,
Trends in
Math. 75-102, Birkhäuser 2007.)
-
Strongly bounded groups and infinite powers of finite
groups. (with unpublished appendices; 8 pages, dvi ,pdf ;ArXiv);
Comm. Algebra 34, 2337-2345, 2006. Note: the first
versions of this paper were untitled "Uncountable groups with
Property (FH)".
Some more papers.
2007-2999
- Compactly presented
groups. (in English; pdf )
- Lectures in Fudan University, Shanghai, July 29 - August 2, 2007:
Large scale simple
connectedness in geometric group theory. (in English; pdf )
2004-2006
- Ma
thèse.
(English with introduction in
French; pdf )
- Semisimple Zariski closure of
Coxeter groups. (in English
dvi ,pdf )
-
Groups with vanishing reduced 1-cohomology. (7 pages,
in
English; dvi
,pdf ).
- Formes
bilinéaires invariantes par une représentation
irréductible réelle. (French,
dvi ,pdf )
- Caractérisation des
groupes
préservant une probabilité sur l'espace projectif
(sur
un
corps
local). (in English; dvi ,pdf )
2001-2003 All papers below were
written
in French
- Une preuve de la classification
des huit géométries modèles de
Thurston de dimension 3. (pdf )
- Une introduction à la
propriété (T) de
Kazhdan. Cet
exposé contient une démonstration du fait que
SL(n,R)
est un groupe de
Kazhdan si n≥3. (dvi ,pdf)
- Une petite introduction au
groupe
symplectique sur R. (dvi ,pdf)
- Le théorème de la borne supérieure de McMullen: il s'agit
d'une
borne supérieure explicite et optimale pour le nombre de faces de
dimension donnée d'un polytope dont on a fixé la dimension et le
nombre de
sommets. C'est dans le cadre de mon mémoire de DEA (2003) que j'ai
rédigé
cette
démonstration, qui fait appel à certaines notions d'algèbre
commutative.
(dvi ,pdf)
- Un exposé sur le spectre du Laplacien d'une variété
Riemannienne: définition et propriétés élémentaires
du Laplacien,
propriétés générales du spectre du Laplacien sur une
variété riemannienne
compacte, calcul dans le cas des sphères et des tores. (dvi ,pdf)
- Un petit article, sur le problème du
prolongement à la frontière d'une
fonction
convexe sur un ouvert de
Rn.(avec Romain Tessera; dvi ,pdf)
- (Novembre 2002) Un exposé élémentaire
sur les
représentations complexes de dimension
finie
de SL(2,R). (dvi
,pdf)
- Un exposé introductif sur les
groupes et algèbres de Lie.
(dvi ,pdf)
- Un calcul de
Hom(ZX,Z): le groupe
abélien libre Z(X) est canoniquement
isomorphe
à son "bidual"
si et seulement si le cardinal de X est inférieur à un cardinal
gigantesque. (dvi ,pdf)
- Un exposé sur le paradoxe de Banach-Tarski et sur les
groupes moyennables discrets:
la duplication de la sphère est essentiellement une conséquence de
la non
moyennabilité du groupe SO(3,R) (vu comme groupe
discret). (dvi ,pdf )
Une page de diverses questions, qui n'est plus très à jour...
Adara, Deneb Kaitos; Albireo;
Procyon B,
Canopus, Arcturus, Zefirka