Bertrand RÉMY

[Service public d'enseignement supérieur et de recherche]


Institut Camille Jordan
UFR de mathématiques - UMR 5208 CNRS / Lyon 1
Bâtiment Jean Braconnier
21 rue Claude Bernard
Université Claude Bernard Lyon 1
69622 Villeurbanne cedex - FRANCE

E-mail: remy at math.univ-lyon1 point fr




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.


Positions.

Junior member of the Institut Universitaire de France since October 2009 (Institut Universitaire de France).

Professor at the Mathematics Institute of the University Lyon 1 - France, since September 2004 (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).


Vita.

You may have a look at my curriculum vitae.


Works.

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 (2002) 29-44, pdf file here.

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.
 
8. with Nicolas 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 Mark 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 Yves Guivarch: Group-theoretic compactification of Bruhat-Tits buildings.  Ann. 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 (2008) 337–352, pdf file here.

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 Peter 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.

18. 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, Soc. Math. de France, 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: On the 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, Preprint # 268 (July 2009), Institut Camille Jordan - Lyon 1, 37 pages, accepted by the J. Inst. Math Jussieu, 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), 46 pages, 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 (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), 55 pages, pdf file here, submitted.


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": a link is here.

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 (2010), with Laurent Bessières and Anne Parreau.

    Contents:

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 (pdf).
        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).



Grants and stays <>

SFB 343 - University of Bielefeld: August 15th - 28th 1999.
ETH Zürich: November 14th - 28th 1999.
University College, London: June 25th - July 22nd 2000 (EPSRC grant).
SFB 343 - University of Bielefeld: July 26th - August 2nd 2000.
Postdoctoral stay at Hebrew University, Jerusalem - academic year 2000 - 2001.
ETH Zürich: June 8th - 23rd 2002.
Université Libre de Bruxelles: March 1st - 7th 2003.
University of Bielefeld: June 19th - 24th 2005.
Institute for Advanced Studies, Princeton (short term visitor): November 19th-26th 2005.
Max-Planck-Institut für Mathematik (Bonn): May 29th-June 9th and July 3rd-7th 2006.
School of mathematical and physical sciences, University of Newcastle (Australia): December 30th 2006 - January 18th 2007.
Mathematics department, Ohio State University: April 2nd-7th 2007.
Mathematical Science Research Institute, Berkeley: October 27th-November 11th 2007.
Mathematics department, University of Michigan (Ann Arbor): April 6th-20th 2008.
Mathematics department, University of Monastir (Tunisia): February 15th-22nd, 2010.


Notes from talks.

<>Year 1997/1998: Workshop "Immeubles" (G. Rousseau supervisor):
    1) Complexes de Coxeter (pdf).
    2) Immeubles euclidiens: constructions métriques  (pdf).
    3) L'immeuble de GL(n) sur un corps p-adique  (pdf).
    4) Systèmes de chambres et systèmes de Tits  (pdf).

Year 1998/1999: Fonction zêta, d'après F. Sato (pdf).

Year 1999/2000: Notes for the PhD defence (pdf).

    Introduction aux immeubles (pdf).

<>Workshop "Compactifications des espaces symétriques" (J.-Ph. Anker supervisor):
    1) Immeuble à l'infini et combinatoire des groupes. Compactification polyédrique des plats (pdf).
    2) Bords et compactifications de Furstenberg (pdf).

Year 2000/2001: Compactifying trees (pdf).

Year 2007/2008: A family of simple groups acting on buildings (MSRI, Berkeley, November 2007), (beamer).

Years 2008/2009 and 2009/2010: colloquium talks in Nancy (March 2009), Rennes (March 2010), Strasbourg (September  2010) and Jussieu (March 2011): Constructions (récentes) de groupes discrets (infinis) simples, (pdf) for the handnotes and (beamer) for the video version (all in French).