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CRM > English > Activities > Conference on Geometrical Analysis
Conference on Geometrical Analysis
Dates: July 1 to 5, 2013

Conformal geometry is the study of the set of angle-preserving (conformal) transformations on a space. While in two dimensions, this is precisely the geometry of Riemann surfaces, in dimensions three and above the answer opens up many new different subjects, leading to the very wide field that is conformal geometry.

The first question is to find conformal invariants, or more specifically, conformally covariant operators, that  is, operators which satisfy some invariant  property under conformal change of metrics on a manifold, and its associated curvature.  The model example is the Laplace-Beltrami operator, in relation to the Yamabe problem.  The Yamabe equation is a second order, semilinear PDE; we would like to understand higher order or fully non-linear generalizations, such as the Paneitz operators together with Q-curvature, or the \sigma_k equation. As a consequence, new interesting directions in PDEs have been opened up, where existence or regularity theory is not developed  as much.

Lately, there has been a lot of interest in the study of non-local, conformally covariant operators of fractional order constructed from Poincaré-Einstein metrics. While they are natural objects in other areas as probability, their geometrical meaning is not yet well understood. Particularly, the study of Poincaré-Einstein metrics has been and continues to be a rich source of activity relating conformal and Riemannian geometry. These are complete
Einstein metrics which are asymptotically hyperbolic at infinity. Their boundary at infinity invariantly inherits a conformal structure. The asymptotic behavior of the metric encodes a great deal of information about the conformal structure at infinity, and this has led to new constructions and progress in conformal geometry. On the other hand, there are many analytic problems concerning the existence, uniqueness and regularity of Poincaré-Einstein metrics with a given conformal infinity and many open problems. This topic is stimulated by its role in the AdS/CFT correspondence in Physics.

In CR geometry there are formal similarities with conformal geometry. For example, there are conformally covariant operators analogous to the conformal Laplacian and the Paneitz operators. While these operators also come with associated Q-curvature quantities, their geometric/analytic meaning is quite different from conformal geometry. The analysis of these operators is closely connected with the geometry of the pseudoconvex manifolds which they may bound, hence of interest in several complex variables.​
List of speakers
Andrea Malchiodi International School for Advanced Studies (SISSA)
Colin Guillarmou Ecole Normale Superieure
Daniel Fox Universidad Politécnica de Madrid
Dmitry Jakobson ​ McGill University
Emmanuel Hebey Université Cergy Pontoise
Fang Wang Princeton University
Gil Solanes Universitat Autònoma de Barcelona
Jeffrey Case Princeton University
Jie Qing University of California at Santa Cruz
Jih-Hsin Cheng Institute of Mathematics - Academia Sinica
Kengo Hirachi The University of Tokyo
Manuel Fernández ​ Universidade de Santiago de Compostela
Manuel Ritoré Universidad de Granada
Matthew Gursky University of Notre Dame
Pablo Mira Universidad Politécnica de Cartagena​
Robert Kusner University of Massachusetts at Amherst
Rod Gover University of Auckland
Spyros Alexakis University of Toronto
Seongtag Kim Inha University, Korea​
Wang Yi Stanford University
Yuxim Ge Université Paris Est Créteil

Organising and Scientific Committee  
Sun-Yung Alice Chang, Princeton University
Maria del Mar González, Universitat Politècnica de Catalunya
Robin Graham, University of Washington
Francisco Martín, Universidad de Granada
Paul Yang, Princeton University​​

Registration includes: attendance to the lectures, documentation package, copy of the course notes, social dinner, and coffee breaks.
Registration fee: 150 €
Reduced registration fee (Phd students and post-docs having read the Thesis in the last three years): 80€

Deadline for registration and payment: June 8th, 2013

IMPORTANT: To register click on one of the Register buttons at the beginning or at the end of the page. ​ ​

 Contributed Talks and posters
If you want to present a poster or give a contributed talk please send an email to Ms Núria Hernandez ( before June 16th with the following information: 
-A title and abstract of your presentation 
-if you would like to present a poster or give a contributed talk

We will send you an e-mail informing you whether your talk has been accepted as soon as a decision has been made by the Scientific Committee.



Participants are encouraged to book their lodging as soon as possible. In case you want to make a reservation at Vila please send a message to Ms. Marta Roig ( Please be sure to mention the reference "CRM Activity" when making your reservation.
Vila Universitària 2

In case you want to make a reservation at Vila please send a message to Ms. Marta Roig ( Please be sure to mention the reference "CRM Activity" when making your reservation.
The following services are included:
Weekly Cleaning service.
  • Water and electricity expenses included in the price.
  • Wire internet connection.
  • Bed and towels equipment.
  • Adapted television to the TDT.
  • Free entrance to SAF (sport facilities)
You can visit the Vila web page at the address: www.vilauniversitaria.comThe address is Vila Universitària, Campus Universitat Autònoma de Barcelona. 08193 Bellaterra. You can check how to get there using the local map of the CRMwebpage: Vila Universitària 2 is right on the campus and the closest train station is Bellaterra train station at the FCG train line.

Hotel Campus
In case you want to make a reservation at Hotel Campus please send a message to Please be sure to mention the reference "CRM Activity" when making your reservation.​

If you have any questions please contact:
Ms. Núria Hernandez
Activities Coordinator​

Sponsors ​

This activity is partially supported by: 


National Science Foundation - Where Discoveries Begin​​