Bertrand RÉMY

[Service public d'enseignement supérieur et de recherche]

Centre de Mathématiques Laurent Schwartz

UMR 7640 du CNRS
École polytechnique
91128 Palaiseau cedex - FRANCE

E-mail: bertrand.remy at


Mathematical interests.

Kac-Moody groups and their twin buildings. 

Tits systems and buildings in general.

S-arithmetic groups and discrete groups in general; related linearity, rigidity and simplicity problems.

Some aspects of geometric group theory.

Bruhat-Tits buildings and their compactifications via various methods.

Totally disconnected locally compact groups.


Professor of mathematics at École polytechnique (on leave from Univ. Lyon) (École polytechnique & CMLS).

Junior member of the Institut Universitaire de France, 2009-2014 (Institut Universitaire de France).

Professor at the Mathematics Institute of the University Lyon 1, 2004-2014 (Institut Camille Jordan).

Habilitation à diriger les recherches (December 2003): Fourier Institute (Grenoble 1) - France (Institut Fourier).

Previous position (September 2001-September 2004): Maître de conférences at the Mathematics Institute of the University Grenoble 1 - France (Institut Fourier).

Academic year 2000/2001: postdoc at the Mathematics Institute of the Hebrew University, Jerusalem - Israel (Einstein Institute).

PhD (September 1999): Mathematics Institute (Élie Cartan Institute) of the University Nancy 1 - France (Institut Élie Cartan).


You may have a look at my curriculum vitae.


1. Construction de réseaux en théorie de Kac-Moody. C. R. Acad. Sc. Paris 329 (1999) 475-478, pdf file here.

2. Immeubles de Kac-Moody hyperboliques. Isomorphismes abstraits entre groupes de même immeuble. Geometriae Dedicata 90, pdf file here.
(2002) 29-44

3. Groupes de Kac-Moody déployés et presque déployés. Astérisque 277 (2002) Société Mathématique de France, 348 pages, pdf file here.

4. Classical and non-linearity properties of Kac-Moody lattices. In "Rigidity in Dynamics and Geometry" (Newton Institute 2000), M. Burger and A. Iozzi eds, Springer (2002) 391-405, pdf file here.

5. Kac-Moody groups: split and relative theories. Lattices. In "Groups: Geometric and Combinatorial Aspects" (Bielefeld 1999), Th. Müller ed, London Math. Soc. Lecture Note Series 311 (2004), Cambridge University Press, 487-541, pdf file here.

6. Topological  simplicity, commensurator superrigidity and non linearity of Kac-Moody groups. Appendix by Patrick Bonvin: Strong boundaries and commensurator superrigidity. Geometric and Functional Analysis 14  (2004) 810-852, pdf file here.

7. Integrability of induction cocycles for Kac-Moody groups. Mathematische Annalen 333 (2005) 29-43, pdf file here.

with N. Monod: Boundedly generated groups with pseudocharacter(s). A 3 page appendix to: Quasi-actions on trees and property (QFA), by J. F. Manning, J. London Math. Soc. (2) 73 (2006) 84-108, pdf file here.

9. with M. Ronan: Topological  groups of Kac-Moody type, right-angled twinnings and their lattices. Commentarii Mathematici Helvetici 81 (2006) 191-219, pdf file here.

10. with P.-E. Caprace: Simplicité abstraite des groupes de Kac-Moody non affines. C. R. Acad. Sc. Paris 342 (2006) 539-544, pdf file here.

11. with Y. Guivarch: Group-theoretic compactification of Bruhat-Tits buildingsAnn. Sci. École Norm. Sup. 39 (2006) 871-920, pdf file here.

12. with U. Baumgartner and George Willis: Flat rank of automorphism groups of buildings. Transf. Groups 12 (2007) 413-436, pdf file here.

13. with U. Baumgartner and J. Ramagge: Contraction groups in complete Kac-Moody groups. Groups, Geometry, and Dynamics 2, pdf file here. (2008) 337–352

14. with P.-E. Caprace: Simplicity and superrigidity of twin buildings lattices. Inventiones Math 176 (2009) 169-221, pdf file here.

15. with P.-E. Caprace: Groups with a root group datum. Innovations in Incidence Geometry 9 (2009) 5-77, pdf file here.

16. with P. Abramenko: Commensurators of some non-uniform tree lattices and Moufang twin trees. Ramanujan Math. Soc. Lecture Note Series 9 (2009) 79-104, pdf file here.

17. Kac-Moody groups as discrete groups. Ramanujan Math. Soc. Lecture Note Series 9 (2009) 105-124, pdf file here.

Covolume des groupes S-arithmétiques et faux plans projectifs, d'après Mumford, Prasad, Klingler, Yeung, Prasad-Yeung, Séminaire Bourbaki, exposé 984 (novembre 2007), in
Astérisque 326 (2010) 83-130, pdf file here.

19. with A. Thuillier and A. Werner: Bruhat-Tits theory from Berkovich's point of view. I: realizations and compactifications of buildings. Ann. Sci. École Norm. Sup. 43 (2010) 461-554, pdf file here.

20. with P.-E. Caprace: Non-distortion of twin building lattices. Geometriae Dedicata 147 (2010) 397-408, pdf file here.

21. with A. Thuillier and A. Werner: Bruhat-Tits theory from Berkovich's point of view. II: Satake compactifications. J. Inst. Math Jussieu11 (2012) 421-465, pdf file here.

22. Groupes algébriques pseudo-réductifs et applications, d’après J. Tits et B. Conrad-O. Gabber-G. Prasad. Séminaire Bourbaki, exposé 1021 (mars 2010), in Astérisque 339 (2011) 259–304, pdf file here.

23. Buildings and Kac-Moody groups, in the proceedings of the conference "Buildings, Finite geometries and Groups" (Bangalore, August 2010), Springer Proceedings in Mathematics 10 (2012), N.S. Narasimha Sastry ed., pp. 222-241, pdf file here.

24. with A. Thuillier and A. Werner: Bruhat-Tits buildings and analytic geometry. Proceedings of the Paris summer school "Berkovich spaces" (July 2010), Antoine Ducros, Charles Favre & Johannes Nicaise editors, Springer Lecture Notes in Mathematics 2119 (2015) 141-202, pdf file here.

with A. Thuillier and A. Werner: Automorphisms of Drinfeld half-spaces over a finite field. Compositio Mathematica 149 (2013) 1211-1224, pdf file here.

26. with P.-E. Caprace: Simplicity of twin tree lattices with non-trivial commutation relations. Preprint Institut Camille Jordan 377, 7 pages, pdf file here, to appear in the proceedings of the Ohio State U. special year on Geometric Group Theory, Springer LNM.

27. with J. Morita: Simplicity of some twin tree automorphism groups with trivial commutation relations
. Canad. Math. Bull. 57 (2014) 390-400, pdf file here.

28. with I. Capdeboscq: On some pro-p groups from infinite-dimensional Lie theory
. Math. Z. 278 (2014) 39-54, pdf file here.

29. On some recent developments in the theory of buildings. Proceedings of the ICM Seoul 2014, to appear, pdf file here.

30. with I. Capdeboscq and A. Lubotzky: Presentations: from Kac-Moody groups to profinite and back. Transf. Groups 21 (2016), pdf file here.

31. with A. Thuillier and A. Werner: Wonderful compactifications of Bruhat-Tits buildings. Preprint (February 2017), pdf file here.

Editorial activity

Editor for the "Annales de l'Institut Fourier": a link for this academic mathematical journal is here.

Editor for the "Journal of Group Theory", 2011-2014.

Editor, with Kenji Iohara and Sophie Morier-Genoud, of the Springer Proceedings in Mathematics & Statistics 40: Symmetries, Integrable Systems and Representations. The book is an outcome of the conferences "Infinite Analysis 11 – Frontier of Integrability" (Univ. Tokyo, July 25th-29th, 2011), and "Symmetries, Integrable Systems and Representations" (Univ. Lyon 1, December 13th-16th, 2011).

Editor, with Laurent Bessières and Anne Parreau, of the proceedings of a Grenoble summer school Non-positively curved geometry, discrete groups and rigidity in the "Séminaires et Congrès" series (Société Mathématique de France), number 18 (2009).


Introduction (pdf).

Résumé (pdf).

1. Quelques groupes et géométries
        Julien Maubon : Riemannian symmetric spaces of the non-compact type: differential geometry (pdf).
        Paul-Émile Paradan : Symmetric spaces of the non-compact type: Lie groups (pdf).
        Guy Rousseau : Euclidean buildings (pdf).
        Yves Benoist : Five lectures on lattices in semisimple Lie groups (pdf).

2. Quelques rigidités en géométrie différentielle
        Gérard Besson : Calabi-Weil rigidity (pdf).
        Marc Bourdon : Quasi-conformal geometry and Mostow rigidity (pdf).
        Laurent Bessières : Minimal volume (pdf).
        Marc Burger and Alessandra Iozzi : A useful formula from bounded cohomology (pdf).

3. Espaces métriques singuliers
        Gilles Courtois : Critical exponents and rigidity in negative curvature
        Cornelia Drutu : Quasi-isometry rigidity of groups (pdf).
        Pierre Pansu : Super-rigidité géométrique et applications harmoniques (pdf).

4. Déformations, espaces de modules et compactifications
        Frédéric Paulin : Sur la compactification de Thurston de l'espace de Teichmüller (pdf).
        Arnaud Beauville : Moduli of cubic surfaces and Hodge theory (pdf).