Objectif The problem of finding canonical Kaehler metrics on compact manifolds is central in Kaehler geometry. Since the pioneering work of Calabi, the existence problem for Kaehler-Einstein (and more generally constant scalar curvature, or even extremal Kaehler) metrics has attracted considerable attention. In this circle of ideas the most fascinating problem is represented by the so-called Yau-Tian-Donaldson conjecture, which predict the equivalence between the K-polystability of a polarized manifold and the existence of a constant scalar curvature (or more generally extremal) Kaehler metric in the polarization class. In this vein we propose the following three main research objectives: first, find an algebraic criterion for K-stability of polarized manifolds; second, study the effect of symplectic reduction on relative K-stability; third study the Calabi flow (in particular on toric manifolds) adapting the La Nave-Tian and Arezzo-La Nave approach to the Kahhler-Ricci flow. We propose to develop the research at Princeton University, under the superfision of prof. G. Tian, and Parma University, under the supervision of prof. C. Arezzo. Champ scientifique natural sciencesmathematicspure mathematicsgeometry Programme(s) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Thème(s) FP7-PEOPLE-2009-IOF - Marie Curie Action: "International Outgoing Fellowships for Career Development" Appel à propositions FP7-PEOPLE-2009-IOF Voir d’autres projets de cet appel Régime de financement MC-IOF - International Outgoing Fellowships (IOF) Coordinateur UNIVERSITA DEGLI STUDI DI PARMA Contribution de l’UE € 228 804,70 Adresse VIA UNIVERSITA 12 43121 PARMA Italie Voir sur la carte Région Nord-Est Emilia-Romagna Parma Type d’activité Higher or Secondary Education Establishments Contact administratif Claudio Arezzo (Prof.) Liens Contacter l’organisation Opens in new window Site web Opens in new window Coût total Aucune donnée
