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Accueil > Agenda > Colloques et rencontres > Archives > Agenda 2005 > Conference on bounded cohomology, harmonic maps and Higgs bundles

Conference on bounded cohomology, harmonic maps and Higgs bundles

Strasbourg and Basel, 14-19 march 2005

Organizers : Olivier Baues (Karlsruhe), Olivier Biquard (Strasbourg), Alessandra Iozzi (Basel and Strasbourg), Anna Wienhard (Basel).

Scope of the conference :
The aim of the conference is to bring together researchers interested in the applications of bounded cohomology, harmonic maps and Higgs bundles to the study of discrete group representations, and to profit from the convergence of ideas which follows from different approaches to similar problems.

Recently progress has been made in several open problems, where rigidity results were proven using methods and techniques either from Higgs bundles, harmonic maps or bounded cohomology. While the different methods lead in certain cases to similar results, sometimes they give only complementary results which do not seem to be easily approachable using other techniques.

For example, some recent and interesting results concern complex hyperbolic lattices and their representations. Arithmeticity of certain lattices was proven by Klingler using Higgs bundles some years ago. Roughly at the same time M.Burger and A.Iozzi have proven an extension of a deformation rigidity result of W.Goldman and J.Millson using bounded cohomology : very recently, the same result has been proven by V.Koziarz and J.Maubon using harmonic maps techniques.

Another very interesting area where a lot of progress has been made in the last year is the study of special components of the variety of representations of surface groups into semisimple Lie groups. F.Labourie, V.Fock and A.Goncharov have obtained very interesting results on the ``Hitchin component’’ of the representation variety, which was defined by Hitchin about 12 years ago using Higgs bundles and studied in certain cases by Goldman using a geometric approach.

There is a connection of the Hitchin component with ``maximal representations’’, which were studied already twenty years ago by Goldman, Toledo and Hernandez using a non-functorial version of bounded cohomology. Recently some results have been obtained by S.Bradlow, O.García-Prada and P.Gothen using Higgs bundles and by M.Burger, A.Iozzi and A.Wienhard using the recent techniques in bounded cohomology introduced by Burger, Monod and Iozzi. Whereas Higgs bundles techniques give information on the number of connected components obtained, the bounded cohomology approach allows to obtain very complete information on the geometry of the maximal representations.

These recent developments exhibit a lot of relations so far not yet understood. We hope that bringing experts of the three different approaches together will help to explore the relations more systematically and will lead to a deeper understanding and further progress.

Invited speakers :
- Steven Bradlow (Higgs bundles and maximal representations, University of Illinois at Urbana-Champaign, U.S.A.)
- Michelle Bucher (bounded cohomology and characteristic classes, Yale University, U.S.A.)
- Marc Burger (deformation rigidity of lattices, maximal representations and bounded cohomology, ETH Zürich, Switzerland)
- Vladimir Fock (Hitchin component, Brown University, U.S.A.) (not confirmed)
- Stefano Francaviglia (volume of representations and simplicial volume, Universitá di Pisa, Italy)
- Koji Fujiwara (bounded cohomology, Tohoku University, Japan)
- Oscar García-Prada (Higgs bundles and maximal representations, Universitat Autonoma de Madrid, Spain)
- William Goldman (maximal representations, University of Maryland, U.S.A.) (not confirmed)
- Alexey Goncharov (Hitchin component, Brown University, U.S.A.)
- Peter Gothen (Higgs bundles and maximal representations, Portugal)
- Luis Hernáandez Lamoneda (maximal representations, CIMAT, Mexico)
- Bruno Klingler (Higgs bundles, rigidity of lattices, University of Chicago, U.S.A.)
- Dieter Kotschick (bounded cohomology and quasi-morphisms, Universität München, Germany) (not confirmed)
- Vincent Koziarz (deformation rigidity of lattices and harmonic maps, Université de Nancy, France)
- Thilo Küssner (bounded cohomology and simplicial volume, Universitäat Siegen, Germany)
- Francois Labourie (Hitchin component, Anosov representations, Université de Paris XI, France)
- Julien Maubon (deformation rigidity of lattices and harmonic maps, Université de Nancy, France)
- Ignasi Mundet i Riera (Higgs bundles, Universitat de Barcelona, Spain)
- Nicolas Monod (bounded cohomology and applications, University of Chicago, U.S.A.)
- HeeSook Park (relative bounded cohomology, Vassar College, U.S.A.)
- Teruhiko Soma (bounded cohomology, Tokyo Denki University, Japan) (not confirmed)
- Domingo Toledo (maximal representations and harmonic maps, University of Utah, U.S.A. and IHES)

Dernière mise à jour le 17-10-2006