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.

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. [Feel free to ask for files]

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

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

3. 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. 

4. Immeubles de Kac-Moody hyperboliques. Isomorphismes abstraits entre groupes de même immeuble. Geometriae Dedicata 90 (2002) 29-44. 

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. 

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.

7. Integrability of induction cocycles for Kac-Moody groups. Mathematische Annalen 333 (2005) 29-43.
 
8. with Mark Ronan: Topological  groups of Kac-Moody type, right-angled twinnings and their lattices. Commentarii Mathematici Helvetici 81 (2006) 191-219.

9. Kac-Moody groups as discrete groups. To appear in the proceedings of "Geometric Group Theory" (Guwahati - Assam, India, December 2002), Hindustan Book Agency, 15 pages (pdf).

10. 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.

11. with Peter Abramenko: Commensurators of some non-uniform tree lattices and Moufang twin trees. To appear in the proceedings of "Geometric Group Theory" (Guwahati - Assam, India, December 2002), Hindustan Book Agency, 23 pages (pdf).

12. with Yves Guivarch: Group-theoretic compactification of Bruhat-Tits buildings.  Ann. Sci. École Norm. Sup. 39 (2006) 871-920.

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

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

15. with P.-E. Caprace: Groups with a root group datum, survey (2008) (pdf), 43 pages, to appear in Innovations in Incidence Geometry.

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

17. Covolume des groupes S-arithmétiques et faux plans projectifs, d'après Mumford, Prasad, Klingler, Yeung, Prasad-Yeung, Séminaire Bourbaki, exposé 984 de novembre 2007, 43 pages (pdf).

18. with P.-E. Caprace: Simplicity and superrigidity of twin buildings lattices. Inventiones Math 176 (2009) 169-221.

19. with A. Thuillier and A. Werner: Bruhat-Tits theory from Berkovich's point of view. I: realizations and compactifications of buildings, Preprint # 245 (March 2009),  Institut Camille Jordan - Lyon 1, (pdf), 79 pages, accepted by the Ann. Sci. École Norm. Sup.

20. with P.-E. Caprace: On the distortion of twin building lattices, Preprint # 267 (August 2009), Institut Camille Jordan - Lyon 1, (pdf), 12 pages, submitted.

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, (pdf), 37 pages, submitted.



Editorial activity

The proceedings of the 2004 Grenoble summer school Non-positively curved geometry, discrete groups and rigidity are now accepted in the "Séminaires et Congrès" series (Société Mathématique de France), number 18.

Editors: Laurent Bessières, Anne Parreau and myself.


    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.


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) au format beamer.