Laboratoire de Mathématiques  (UMR 6205)

Laboratoire de  Mathématiques et Physique théorique (UMR 6083)

Conformal Geometry :

 invariant theory and the variational method









Roscoff , France 


June 30 - July 4, 2008































 An international conference devoted to conformal
geometry will be held at the Station Biologique
de Roscoff (CNRS), under the auspices of the  Department of
Mathematics of the 
University of Bretagne Occidentale and the ANR " Flots et
Opérateurs
Géométriques ".  


Conformal geometry is one of the founding themes of modern differential
geometry and geometric analysis.  One can cite the theorem of
Riemann which states that any surface is conformal to one of constant
curvature; as a consequence we have the classification of compact
surfaces as quotients of a model geometry by a group of
isometries.  The generalization of this theorem to manifolds
of
arbitrary dimension: find a metric conformal to a given one with
constant scalar curvature, is known as the Yamabe problem and has
motivated much of the development in geometric analysis over the last
twenty five years.  However, the scalar curvature is not
sufficiently discerning in higher dimensions to characterize the
topology of manifolds and other quantities, such as Q-curvature seem to
play a vital role. 





On the other hand, one has the theory of conformal invariants:
differential operators which remain invariant (up to multiple by a
scalar field) after a conformal deformation of the
metric.  
The most fundamental example is the Laplace operator in dimension
2.  Others include the conformal Laplacian, the Paneitz
operator
in dimension 4 and its generalization to arbitrary even
dimensions.  Related to these operators one finds a rich
interaction with other domains such as spectral theory and quantum
field theory.  Objects such as the zeta-regularized
determinant
arise, as well as a diverse array of functionals and related quantities
like the Schouten tensor and Q-curvature.





The aim of  this conference is to bring together experts in
these
fields, as well as people working in neighbouring domains, in order to
exchange ideas and to recount some of the latest advances.  We
do
not expect to be constrained by the title and look forward to
excursions into unfamiliar territory.  Doctoral students and
young
researchers are particularly encouraged to attend, and we hope that all
participants will gain inspiration from this meeting. 







SCIENTIFIC COMMITTEE
 



 G.
Besson  (Univ. Grenoble),  M.
Eastwood
 (Univ. Adelaïde), M. Struwe (ETH
Zurich) 












ORGANIZING COMMITTEE
  



 P.
Baird
 (Univ. Brest) , 
A. El Soufi (Univ. Tours), A. Fardoun
(Univ. Brest) , R.
Regbaoui
(Univ. Brest) 












 LIST OF MAIN SPEAKERS 
 


 
           
       
            



 


A. Cap (Univ. Vienne)


  


G. Carron (Univ. Nantes)


  


J. Choe (KIAS, Korea)


  


B. Colbois (Univ. Neuchatel)


  


Z. Djadli (Univ. Grenoble)


  


A. Gastel (Friedrich-Alexander-Universität)


  


R. Gover (Univ. Auckland) 


  


R. Graham  (Univ. Washington) 


  


M. Gursky (Univ. Notre Dame)  


  


F. Hélein (Univ. Paris VII) 


  


K. Hirachi (Univ. Tokyo)


  


D. Knopf (Univ. Texas, Austin) 


  


C. LeBrun (Univ. Stony Brook) 


  


A. Malchiodi (SISSA, Trieste)


  


R. Mazzeo (Stanford Univ. ) 


  


N. Nadirashvili (Univ. Marseille)


  


S. Nishikawa (Tohoku Univ. ) 


  


F. Pacard (Univ. Paris XII)


  


F. Pedit (Univ. Tübingen)


  


T. Rivière (ETH Zurich )


  


F. Robert (Univ. Nice) 


  


U. Simon (Technische Univ. ,  Berlin)


  


H. Urakawa (Tohoku Univ. ) 


  


  J. C. Wood (Univ. Leeds)


   


  S. Yamada (Tohoku Univ. ) 


  


  


  








  LOCATION 
 





The conference will take place at the  Station Biologique
de Roscoff (CNRS). This is a beautiful location overlooking
the sea in Roscoff about
40 kilometers away from Brest
in the heart of Brittany. The centre boasts a panoramic restaurant, a
large lecture hall, as well as computer facilities with internet
access. Accommodation is on-site, with each room having its own
facilities. Participants will have the opportunity to sample local
seafood in some fine restaurants and if they wish, to participate in
nautical recreation activities. An additional interest this year is
that the Tour
de France
begins at Brest on Saturday July 5th (the Saturday following the
conference). Soon after the conference (from July 11th - July 17th)
there is a maritime
festival that will take place at Brest, which includes the
arrival of the tall ships
















  

    


      
      

      


      


      		

      
      

      


      


      		

      
      

      


      


      		

      
      

      


      


      		

      
      

      


      


      		

    


  









Ce projet bénéficie du soutien financier du
conseil
régional de Bretagne,  du conseil
général du
Finistère et de Brest Métropole
Océane.