Geometry and dynamics via contact topology

Objectif

I intend to cross ressources of holomorphic curves techniques and traditional topological methods to study some fundamental questions in symplectic and contact geometry such as:

- The Weinstein conjecture in dimension greater than 3.
- The construction of new invariants for both smooth manifolds and Legendrian/contact manifolds, in particular, try to define an analogue of Heegaard Floer homology in dimension larger than 3.
- The link, in dimension 3, between the geometry of the ambient manifold (especially hyperbolicity) and the dynamical/topological properties of its Reeb vector fields and contact structures.
- The topological characterization of odd-dimensional manifolds admitting a contact structure.

A crucial ingredient of my program is to understand the key role played by open book decompositions in dimensions larger than three.

This program requires a huge amount of mathematical knowledges. My idea is to organize a team around Ghiggini, Laudenbach, Rollin, Sandon and myself, augmented by two post-docs and one PhD student funded by the project. This will give us the critical size to organize a very active working seminar and to have a worldwide attractivity and recognition.
I also plan to invite one confirmed researcher every year (for 1-2 months), to organize one conference and one summer school, as well as several focused weeks.

Champ scientifique

Régime de financement

ERC-SG - ERC Starting Grant

Coordinateur

UNIVERSITE DE NANTES

Adresse

Quai de tourville 1
44035 Nantes cedex 1
France

Région

Pays de la Loire Pays de la Loire Loire-Atlantique

Type d’activité

Higher or Secondary Education Establishments

Chercheur principal

Vincent Maurice Colin (Mr.)

Contact administratif

Elodie Hervio (Ms.)

Liens

Contacter l’organisation Site web

Contribution de l’UE

Aucune donnée

Bénéficiaires (1)

UNIVERSITE DE NANTES

France