Des maths...

My list of publications on MathSciNet (MathSciNet searches on Author = "Cornulier" or "de Cornulier" result in partial lists)

Main survey works.

• (with Pierre de la Harpe) Metric geometry of locally compact groups (book, pdf version of July 2016, 233 pages; EMS Tracts in Mathematics Vol. 25, European Math. Society, September 2016. Book at EMS' site) Erratum. Note: the first version of this book was entitled "A metric panorama of locally compact groups". Here is more informal and shorter survey: Zooming in on the large-scale geometry of locally compact groups (14 pages, pdf)
• Groupes pleins-topologiques, d'après Matui, Juschenko-Monod…, written exposition of the Bourbaki Seminar of January 19th, 2013 (in French; pdf, 39 pages) In: Séminaire Bourbaki, volume 2012/2013, exposés 1059-1073 Astérisque 361 (2014)
• On the quasi-isometric classification of locally compact groups (51 pages, pdf). Pages 275-342 in: New directions in locally compact groups (P-E. Caprace, N. Monod edts), London Math. Soc. Lecture Notes Series 447, Cambridge University Press 2018. Note: the first versions of this paper were entitled " On the quasi-isometric classification of focal hyperbolic groups".
• Group actions with commensurated subsets, wallings and cubings. (82 pages, pdf). Summarizing slides: (Commensurating actions, Properties FW and PW: pdf)

Mémoire d'habilitation à diriger les recherches (HDR) (15 mai 2014, in French, 36 pages) This is a summary of part of the research performed after PhD, until the habilitation defense. In the French system, the HDR diploma is required in order to supervise PhD students.

Publications, submitted papers and prepublications.
Reminder: in accordance to the custom in mathematics, the authors of an article are systematically listed in alphabetical order. In particular, the use of "Alpha et al." in bibliographies should be avoided, and the listing of articles by Google mentioning only the first named author should be considered as a damaging nuisance.

• Near actions (169 pages, pdf)
• (with Octave Lacourte) On groups of rectangle exchange transformations (35 pages, pdf)
• Realizations of groups of piecewise continuous transformations of the circle (23 pages, pdf, J. Mod. Dyn. 16 (2020), 59-80)
• On the space of ends of infinitely generated groups (27 pages, pdf), Topology Appl. 263 (2019) 279-298.
• Property FW and 1-dimensional piecewise groups (10 pages, pdf), C. R. Math. Acad. Sci. Paris 359 (2021), 71-78.
• Commensurating actions for groups of piecewise continuous transformations (66 pages, pdf), Ann. H. Lebesgue 4 (2021), 1457-1520.
• The papers "Regularization of birational actions of FW groups", and the paper with Serge Cantat "Commensurating actions of birational groups and groups of pseudo-automorphisms", classified below in "birational transformations" also deal with commensurating actions.
• The survey "Group actions with commensurated subsets..." linked above of course belongs on this category.
• Irreducible lattices, invariant means, and commensurating actions. (31 pages, pdf), Math. Z. 279(1) (2015) 1-26.
• (with Yves Stalder and Alain Valette) Proper actions of wreath products and generalizations. (28 pages, pdf), Trans. Amer. Math. Soc 364 (2012), 3159-3184.
• (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.

• Gradings on Lie algebras, systolic growth, and cohopfian properties of nilpotent groups (48 pages, pdf, Bull. Soc. Math. France 144(4) (2016) 693-744) Note: the first version of this paper was entitled "Carnot Lie algebras, field extensions, and systolic growth".
• On the Koszul map of Lie algebras (39 pages, pdf, Forum Math. 28 (2016), no. 1, 101-128.)
• Nilpotent Lie algebras and systolic growth of nilmanifolds (31 pages, pdf), Int. Math. Res. Not. IMRN 2019, no. 9, 2763-2799.
• The paper below with Romain Tessera "Geometric presentations of Lie groups and their Dehn functions" also includes entire sections devoted to Lie algebras, as well as the paper "On sublinear bilipschitz equivalence of groups".

• On sublinear bilipschitz equivalence of groups (pdf), Ann. ENS. 52, no 5, (2019) 1201-1242.
• (with Adrien Le Boudec) Densely related groups (28 pages, arXiv link), Ann. Fac. Sci. Toulouse Math. (Sér. 6) 28(4) (2019) 619-653.
• (with Romain Tessera) Geometric presentations of Lie groups and their Dehn functions (137 pages, pdf), Publ. Math. IHES 125(1) (2017), 79-219. Here is a substitute of review.
• Commability and focal locally compact groups (26 pages, pdf), Indiana Univ. Math. J. 64(1) (2015) 115-150. Note: the first versions of this paper were entitled "Commability and focal groups" and "On the commability and quasi-isometry classification of focal groups".
• (with Pierre-Emmanuel Caprace, Nicolas Monod, and Romain Tessera) Amenable hyperbolic groups (40 pages, pdf), J. Eur. Math. Soc. 17 (2015), 2903-2947.
• (with Romain Tessera) Dehn function and asymptotic cones of Abels' group (27 pages, pdf), J. Topology 6(4) (2013), 982-1008.
• (with Indira Chatterji, Guido Mislin, and Christophe Pittet) Bounded characteristic classes and flat bundles. (12 pages, pdf), J. Differential Geom. 95(1) (2013), 39-51.
• (with David Fisher and Neeraj Kashyap) Cross-wired lamplighter groups (10 pages, pdf), New York J. Math. 18 (2012) 667-677.
• (with Romain Tessera) Contracting automorphisms and L^p-cohomology in degree one. (27 pages, pdf), Ark. Mat. 49(2) (2011) 295-324.
• Asymptotic cones of Lie groups and cone equivalences. (22 pages, pdf), Illinois J. Math. 55(1) (2011), 237-259.
• (with Romain Tessera) Metabelian groups with quadratic Dehn function and Baumslag-Solitar groups. (13 pages, pdf), Confluentes Math., Vol. 2, No. 4 (2010) 431-443. Note: the first versions of this paper were entitled "Embeddings of solvable Baumslag-Solitar groups into discrete groups with quadratic Dehn function".
• 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.

• (with Romain Tessera) On the vanishing of reduced 1-cohomology for Banachic representations. (43 pages, pdf), Ann. Inst. Fourier 70 (2020), no. 5, 1951-2003.
• (with Alain Valette) On equivariant embeddings of generalized Baumslag-Solitar groups (24 pages, pdf), Geom. Dedicata 175 (2015) 385-401.
• (with Romain Tessera) A characterization of relative Kazhdan Property T for semidirect products with abelian groups. (16 pages, pdf), Ergodic Theory Dynam. Systems 31 (2011), 793-805.
• (with Bachir Bekka) A spectral gap property for subgroups of finite covolume in Lie groups. (9 pages, pdf), Colloquium Math. 118 (2010) 175-182.
• Both papers with Yves Stalder and Alain Valette, classified here in "commensurating actions", deal with the Haagerup Property too.
• (with Raf Cluckers, Nicolas Louvet, Romain Tessera, and Alain Valette) The Howe-Moore property for real and p-adic groups. (25 pages, pdf), Math. Scand. 109(2) (2011) 201-224.
• (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 Banach spaces and representations vanishing at infinity. (28 pages, pdf ); Transform. Groups 13 (2008), no. 1, 125--147.
• (with Romain Tessera and Alain Valette) Isometric group actions on Hilbert spaces: growth of cocycles. (24 pages, pdf ), Geom. Funct. Anal. 17 (2007), 770-792.
• 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 entitled "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.

      ▬ Chabauty topology (space of marked groups, spaces of subgroups, etc.)
• Counting submodules of a module over a noetherian commutative ring (34 pages, pdf), J. Algebra 534 (2019), 392-426.
• Subgroups approximatively of finite index and wreath products (13 pages, pdf, special volume for P. de la Harpe's 70th birthday: Groups Geom. Dyn. 8 (2014), no. 3, 775-788)
• (with Robert Bieri, Luc Guyot, and Ralph Strebel) Infinite presentability of groups and condensation. (32 pages, pdf), J. Inst. Math. Jussieu 13(4) (2014) 811-848. Note: a previous version of this paper, authored by YC and Luc Guyot (12 pages), was entitled On infinitely presented soluble groups.
• On the Chabauty space of locally compact abelian groups. (24 pages, pdf), Algebr. Geom. Topol. 11 (2011) 2007-2035.
• On the Cantor-Bendixson rank of metabelian groups. (20 pages, pdf), Ann. Inst. Fourier 61(2) (2011), 593-618.
• (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.
• A sofic group away from amenable groups. (6 pages, pdf), Math. Ann. 350(2) (2011) 269-275.
• The space of finitely generated rings. (8 pages, pdf ), Internat. J. Algebra Comput. 19(3) (2009) 373-382.
• (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.
  
        ▬ Groups of birational transformations, etc.
• Regularization of birational actions of FW groups (9 pages, pdf) Confluentes Mathematici, Tome 12 (2020) no. 2, pp. 3-10.
• (with Serge Cantat) Distortion in Cremona group (32 pages, ArXiv link), Ann. Sc. Norm. Sup. Pisa Cl. Sci. (5) 20 (2020), no. 2, 827-858.
• (with Serge Cantat) Commensurating actions of birational groups and groups of pseudo-automorphisms (41 pages, pdf), J. Éc. polytech. Math. 6 (2019) 767-809.
• Sofic profile and computability of Cremona groups (20 pages, pdf), Michigan Math. J. 62(4) (2013) 823-841.
• The Cremona group is not an amalgam Appendix to the paper by Serge Cantat and Stéphane Lamy Normal subgroups in the Cremona group, Acta Math. 210 (2013), no. 1, 31-94 (appendix: pages 88-92). (appendix: pdf, 5 pages)
• (with Mikhail Borovoi) Conjugate complex homogeneous spaces with non-isomorphic fundamental groups (arXiv link) C. R. Math. Acad. Sci. Paris 353 (2015), no. 11, 1001-1005.
• Nonlinearity of some subgroups of the planar Cremona group (7 pages, pdf)
  
        ▬ Locally compact groups, etc.
• Locally compact wreath products. (23 pages, pdf), J. Austral. Math. Soc. 107(1) (2019), 26-52.
• (with Pierre-Emmanuel Caprace) On embeddings into compactly generated groups. (14 pages, pdf), Pacific J. Math. 269(2) (2014) 305-321.
• On lengths on semisimple groups. (9 pages, pdf); J. Topol. Anal. 1(2) (2009) 113-121.
• Strong boundedness of Homeo(Sⁿ). Appendix to Distortion in transformation groups by Danny Calegari and Michael H. Freedman. (pdf); Geom. Topol. 10 (2006), 267-293 (appendix p.290).
• Strongly bounded groups and infinite powers of finite groups. (with two unpublished appendices; 8 pages, dvi ,pdf ;ArXiv); Comm. Algebra 34, 2337-2345, 2006. Note: the first versions of this paper were entitled "Uncountable groups with Property (FH)".
  
        ▬ Discrete groups
• (with John S. Wilson) First-order recognisability in finite and pseudofinite groups (16 pages, arXiv link, J. Symb. Log. 85 (2020), no. 2, 852-867)
• (with Agnieska Bier and Piotr Słalina) On groups with weak Sierpiński subsets (arXiv), Fund. Math. 252 (2021), no. 2, 171-178.
• (with Laurent Bartholdi and Dessislava Kochloukova) Homological finiteness properties of wreath products (arXiv link) Quarterly. J. Math. 66 (2015), no. 2, 437-457.
• (with Khalid Bou-Rabee) Systolic growth of linear groups (5 pages, pdf), Proc. Amer. Math. Soc. 144 (2016), no. 2, 529-533.
• (with Emmanuel Breuillard, Alex Lubotzky, and Chen Meiri) On conjugacy growth of linear groups. (21 pages, pdf), Math. Proc. Cambridge Philos. Soc. 154(2) (2013), 261-277.
• (with Emmanuel Breuillard) On conjugacy growth for solvable groups. (7 pages, pdf), Illinois J. Math. 54(1) (2010), 389-395.
• (with Aditi Kar) On Property (FA) for wreath products. (8 pages, pdf), J. Group Theory 14(1) (2011) 165-174.
• Infinite conjugacy classes in groups acting on trees. (9 pages, 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.)
• 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, pdf ); Geometric Group Theory, Trends in Math. 75-102, Birkhäuser 2007.)

Some more unpublished papers and lecture notes.

2007-2999
• Near actions (lectures in IMPAN, Warsaw, April 2019): pdf, 22 pages and many figures.
• A course in Lie algebras (based on 12-hour lectures in automn 2018) pdf, 37 pages.
• Exemples de groupes non C^*-simples, d'après Haagerup-Olesen et Le Boudec (notes d'un groupe de travail) pdf
• Slides on commensurating actions, Properties FW and PW, pdf, 2012.
• Lectures in Shanghai on Kazhdan's Property T, Noncommutative geometry meeting, July 2012 (in English, 24 pages, pdf).
• Notes on groups with exponential Dehn function (5 pages, in English pdf)
• Property T for linear groups over rings, after Shalom (Feb. 2007, 4 pages, in English; pdf)
• Fixed points and almost fixed points, after Gromov and V. Lafforgue (Dec. 2006, 3 pages, in English; pdf)
• 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 ) These two lectures notes were eventually expanded into the book published with Pierre de la Harpe.
  
  2004-2006
• Ma thèse (décembre 2005). (English with introduction in French; pdf )
• Semisimple Zariski closure of Coxeter groups. (6 pages, in English; pdf , arXiv math/1211.5635)
• Groups with vanishing reduced 1-cohomology. (7 pages, in English; dvi ,pdf ).
• A note on quotients of word hyperbolic groups with Property (T) (in English, 2 pages, arXiv math/0405193)
• 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 (mai 2003, encadrement Raphaël Rouquier) 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)
• (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). Exposé de maîtrise (M1) encadré par Yves Coudène, juin 2001 (dvi ,pdf )