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 polytechnique.edu


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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 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).



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, 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.
 

8.
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.

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, 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.

25.
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, 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. Épijournal de Géométrie Algébrique, volume 1 (2017), article 10, 18 pages, pdf file here.

32. with M. Bourdon: Quasi-isometric invariance of continuous group L^p-cohomology, and first applications to vanishings, preprint (March 2018), 35 pages, 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).

    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).