CCEM - Contraintes de Courbure et Espaces des Métriques

Project ANR-17-CE40-0034

CCEM is a research project founded by Agence Nationale de la Recherche, 2018-2022.

Presentation

A fundamental problem in Riemannian geometry is to understand "spaces of metrics" satisfying variours curvature constraints. These spaces can be endowed with topologies, as the Gromov-Hausdorff one. When non compact it is natural to try to complete them by introducing singular metrics. This has led to the definition of several classes of singular metric spaces, studied for their links to Riemannian manifolds but also for themselves. Our project gather geometers specialists in topology, Ricci flow, analysis on manifolds and sungular metrics spaces, with the aim to study these spaces of Riemannian or generalized metrics by combining our approaches and techniques. We envision questions of existence-uniqueness of "best metric" in a given class, of homotopy type of classes of metrics, generalisations of the theory of limits under Ricci bounds, as well as the study of some stratified spaces with conical iterated metrics.

Our team

The project consortium is divided in four partners: Bordeaux (coord. Laurent Bessières), Grenoble (coord. Gérard Besson ), Montpellier (coord. Philippe Castillon) and Nantes (coord. Samuel Tapie ). The research institutions that will host our project are the Institut de Mathématiques de Bordeaux, Institut Fourier , Institut Montpelliérain Alexander Grothendieck and Laboratoire mathématique Jean Leray , respectively.
The other members of the team are Jérôme Bertrand (Toulouse), Gilles Carron (Nantes), Erwann Delay (Avignon), Alix Deruelle (UPMC), Gautier Dietrich (Montpellier), Marc Herzlich (Montpellier), Sylvain Maillot (Montpellier), Ilaria Mondello (UPEC), Thomas Richard (UPEC), Berardo Ruffini (Montpellier), Arnaud Stoker (Grenoble), Constantin Vernicos (Montpellier), Jian Wang (Grenoble).
Post-doctoral positions funded by the project will be available in Nantes and Montpellier.

Activities

The beginning of our scientific project is of February 1st, 2018.
We schedule our first team meeting in Montpellier, May 2-4, 2018. The program
Our second meeting will be held at Paris-Est-Créteil University, November 21-23, 2018. The program
Our third meeting is scheduled in Nantes, April 10-12, 2019. The program
The first Master class of our project will be held at IHP, May 27-31, 2019. It is devoted to the structure of limit spaces. Details here : Master class in differential geometry: the structure of limit spaces
Our fourth meeting is held in Toulouse, November 27-29, 2019. The program
~~Our next meeting is scheduled in Avignon, April 22-24, 2020.~~
~~The second Master class of our project will be held at IHP, June 29-July 3, 2020. It is devoted to spaces with curvature bounded below. Details below :~~

Our fifth meeting is held in Montpellier, October 12-14, 2020. The program
Our sixth meeting is held in Avignon, November 15-17, 2021. The program
Our seventh meeting is held in Bordeaux, May 9-11, 2022. The program
Our eight meeting is held in Nancy, September 7-9, 2022. The program
Our last meeting is held in Créteil, Jenuary 11-13, 2023. The program

Master Class & Summer School

Our ANR project participates to the organization of the Fourier Institute Summer School, held in Grenoble, June 14-July 2 2021, in an hybrid mode:

~~Our ANR project organizes at IHP a second Master class in differential geometry, June 29-July 3 2020 :~~