CAMEGEST

Extremal Kaehler metrics and geometric stability

Coordinatore	UNIVERSITA DEGLI STUDI DI PARMA    more  Organization address address: VIA UNIVERSITA 12 city: PARMA postcode: 43100 contact info Titolo: Prof. Nome: Claudio Cognome: Arezzo Email: send email Telefono: +39 0521 906949 Fax: +39 0521 906950
Nazionalità Coordinatore	Italy [IT]
Totale costo	228˙804 €
EC contributo	228˙804 €
Programma	FP7-PEOPLE Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013)
Code Call	FP7-PEOPLE-2009-IOF
Funding Scheme	MC-IOF
Anno di inizio	2010
Periodo (anno-mese-giorno)	2010-09-15   -   2013-09-14

 Partecipanti

#	participant	country	role	EC contrib. [€]
1	UNIVERSITA DEGLI STUDI DI PARMA  Organization address address: VIA UNIVERSITA 12 city: PARMA postcode: 43100 contact info Titolo: Prof. Nome: Claudio Cognome: Arezzo Email: send email Telefono: +39 0521 906949 Fax: +39 0521 906950	IT (PARMA)	coordinator	228˙804.70

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 Obiettivo del progetto (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.'