Objective 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. Fields of science 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) Topic(s) FP7-PEOPLE-2009-IOF - Marie Curie Action: "International Outgoing Fellowships for Career Development" Call for proposal FP7-PEOPLE-2009-IOF See other projects for this call Funding Scheme MC-IOF - International Outgoing Fellowships (IOF) Coordinator UNIVERSITA DEGLI STUDI DI PARMA EU contribution € 228 804,70 Address VIA UNIVERSITA 12 43121 PARMA Italy See on map Region Nord-Est Emilia-Romagna Parma Activity type Higher or Secondary Education Establishments Administrative Contact Claudio Arezzo (Prof.) Links Contact the organisation Opens in new window Website Opens in new window Total cost No data
