Objectif The purpose of this project is to study basic questions in algebraic and Kähler geometry. It is well known that the structure of projective or Kähler manifolds is governed by positivity or negativity properties of the curvature tensor. However, many fundamental problems are still wide open. Since the mid 1980's, I have developed a large number of key concepts and results that have led to important progress in transcendental algebraic geometry. Let me mention the discovery of holomorphic Morse inequalities, systematic applications of L² estimates with singular hermitian metrics, and a much improved understanding of Monge-Ampère equations and of singularities of plurisuharmonic functions. My first goal will be to investigate the Green-Griffiths-Lang conjecture asserting that an entire curve drawn in a variety of general type is algebraically degenerate. The subject is intimately related to important questions concerning Diophantine equations, especially higher dimensional generalizations of Faltings' theorem - the so-called Vojta program. One can rely here on a breakthrough I made in 2010, showing that all such entire curves must satisfy algebraic differential equations. A second closely related area of research of this project is the analysis of the structure of projective or compact Kähler manifolds. It can be seen as a generalization of the classification theory of surfaces by Kodaira, and of the more recent results for dimension 3 (Kawamata, Kollár, Mori, Shokurov, ...) to other dimensions. My plan is to combine powerful recent results obtained on the duality of positive cohomology cones with an analysis of the instability of the tangent bundle, i.e. of the Harder-Narasimhan filtration. On these ground-breaking questions, I intend to go much further and to enhance my national and international collaborations. These subjects already attract many young researchers and postdocs throughout the world, and the grant could be used to create even stronger interactions. Champ scientifique natural sciencesmathematicspure mathematicsmathematical analysisdifferential equationsnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Thème(s) ERC-ADG-2014 - ERC Advanced Grant Appel à propositions ERC-2014-ADG Voir d’autres projets de cet appel Régime de financement ERC-ADG - Advanced Grant Institution d’accueil UNIVERSITE GRENOBLE ALPES Contribution nette de l'UE € 1 809 345,00 Adresse 621 AVENUE CENTRALE 38058 Grenoble France Voir sur la carte Région Auvergne-Rhône-Alpes Rhône-Alpes Isère Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 809 345,01 Bénéficiaires (1) Trier par ordre alphabétique Trier par contribution nette de l'UE Tout développer Tout réduire UNIVERSITE GRENOBLE ALPES France Contribution nette de l'UE € 1 809 345,00 Adresse 621 AVENUE CENTRALE 38058 Grenoble Voir sur la carte Région Auvergne-Rhône-Alpes Rhône-Alpes Isère Type d’activité Higher or Secondary Education Establishments Liens Contacter l’organisation Opens in new window Participation aux programmes de R&I de l'UE Opens in new window Réseau de collaboration HORIZON Opens in new window Coût total € 1 809 345,01
