Des maths...

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 L^p-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(Z^X,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 )