2022-05018 - Doctorant F/H Isoperimetric inequalities of convex projective geometries and applications

Type de contrat : CDD

Niveau de diplôme exigé : Bac + 5 ou équivalent

Fonction : Doctorant

A propos du centre ou de la direction fonctionnelle

Located at the heart of the main national research and higher education cluster, member of the Université Paris Saclay, a major actor in the French Investments for the Future Programme (Idex, LabEx, IRT, Equipex) and partner of the main establishments present on the plateau, the centre is particularly active in three major areas: data and knowledge; safety, security and reliability; modelling, simulation and optimisation (with priority given to energy).   

The 450 researchers and engineers from Inria and its partners who work in the research centre's 28 teams, the 60 research support staff members, the high-level equipment at their disposal (image walls, high-performance computing clusters, sensor networks), and the privileged relationships with prestigious industrial partners, all make Inria Saclay Île-de-France a key research centre in the local landscape and one that is oriented towards Europe and the world.

Contexte et atouts du poste

The Hilbert and Thompson metric are a fundamental class of Finsler metrics,
and their geometry is closely tied to the one of convex bodies. They are a basic tool in the study
of non-expansive dynamic systems (non-linear Perron-Frobenius theory, generalizations of the Wolff-Denjoy theorem) and also in optimization,
in the analysis of interior point methods. Additional motivations arise from recent develops in
tropical geometry, aiming at extending Hilbert metrics in a non-archimedean setting, in relation with complexity problems for zero-sum games.

Mission confiée

The goal of this PhD subject is to develop a theory of isoperimetric inequalities for the
Hilbert and Thompson metric in convex domains, in interaction with the application fields (optimization and games) in which these metrics arise. See the detailed subject
for more information.

Compétences

Some background in one of the following mathematical fields: convex analysis, differential geometry, tropical geometry, metric geometry, or optimization will be appreciated.

Avantages

  • Restauration subventionnée
  • Transports publics remboursés partiellement
  • Congés: 7 semaines de congés annuels + 10 jours de RTT (base temps plein) + possibilité d'autorisations d'absence exceptionnelle (ex : enfants malades, déménagement)
  • Possibilité de télétravail (après 6 mois d'ancienneté) et aménagement du temps de travail
  • Équipements professionnels à disposition (visioconférence, prêts de matériels informatiques, etc.)
  • Prestations sociales, culturelles et sportives (Association de gestion des œuvres sociales d'Inria)
  • Accès à la formation professionnelle
  • Sécurité sociale

Rémunération

monthly gross salary : 1st et 2nd year 1982€ and 3rd year 2085€