From complex to non-archimedean geometry

Objectif

"Complex geometry is the study of manifolds that are defined over the complex numbers. Non-archimedean geometry is concerned with analytic spaces over
fields endowed with a norm that satisfies the strong triangular inequality.
The aim of this proposal is to explore the interactions between these seemingly different geometries
with special emphasis on analytic and dynamical problems.

We specifically plan to develop pluripotential theory over non-archimedean fields. This includes the search for analogs of the celebrated Yau's theorem. In a more local setting, we shall also look for possible applications of non-archimedean techniques to the ""Openness Conjecture"" on the structure of singularities of plurisubharmonic functions.

A second axis of research concerns the problem of growth of degrees of iterates of complex rational maps in arbitrary dimensions. We especially aim at extending to arbitrary dimensions the successful non-archimedean techniques that are already available for surfaces.

Finally we want to investigate the geometry of parameter spaces of complex dynamical systems
acting on the Riemann sphere using non-archimedean methods. This requires the development of the bifurcation theory of non-archimedean rational maps."

Champ scientifique

Régime de financement

ERC-SG - ERC Starting Grant

Institution d’accueil

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS

Contribution de l’UE

€ 787 232,52

Adresse

RUE MICHEL ANGE 3
75794 Paris
France

Région

Ile-de-France Ile-de-France Paris

Type d’activité

Research Organisations

Chercheur principal

Charles Favre (Mr.)

Contact administratif

Bertrand Minault (Mr.)

Liens

Contacter l’organisation Site web

Coût total

Aucune donnée

Bénéficiaires (1)