Obiettivo "This proposal centers on the special interaction of algebraic and differential geometry which arises from the notion of stability, going back to the celebrated correspondence between polystable vector bundles and Hermite-Einstein connections.A conjecture of Yau, Tian and Donaldson seeks to extend this correspondence to projective manifolds, formulating an algebro-geometric notion of stability (K-polystability) which should be equivalent to the existence of a (unique) Kaehler metric of constant scalar curvature in the first Chern class of an ample line bundle. The necessity of stability is now settled, thanks to the work of Donaldson, myself (Adv. in Math. 2009) and Mabuchi. The existence implication however seems to be out of reach with current techniques. In this project I will motivate the need to go beyond the notion of K-stability, and select some crucial open problems which arise naturally in this context, especially in connection with Donaldson's program for Fano manifolds and his conjecture that a Fano manifold with a Kaehler-Einstein metric is ``birationally stable"". Another surprising application of algebro-geometric stability to differential geometry has recently emerged in the physical work of Gaiotto, Moore and Neitzke. They showed (conjecturally) how to use the stability and wall-crossing of ``BPS states'' to reconstruct the Hitchin hyperkaehler metric on a class of moduli spaces of Higgs bundles. In this project I propose to study some exciting mathematical questions which arise from this theory.This project aims at attacking some central problems which stem from the connection between stability and special metrics, and will be carried out by myself as P.I. and Gabor Szekelyhidi as a Team Member, over a period of four years. We will be supported by two Post-Docs (each position lasting two years) and a graduate student (three years)." Campo scientifico natural sciencesmathematicspure mathematicsgeometry Programma(i) FP7-IDEAS-ERC - Specific programme: "Ideas" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Argomento(i) ERC-SG-PE1 - ERC Starting Grant - Mathematical foundations Invito a presentare proposte ERC-2012-StG_20111012 Vedi altri progetti per questo bando Meccanismo di finanziamento ERC-SG - ERC Starting Grant Istituzione ospitante SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE Contributo UE € 124 408,70 Indirizzo VIA BONOMEA 265 34136 Trieste Italia Mostra sulla mappa Regione Nord-Est Friuli-Venezia Giulia Trieste Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Jacopo Stoppa (Dr.) Contatto amministrativo Gabriele Rizzetto (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato Beneficiari (2) Classifica in ordine alfabetico Classifica per Contributo UE Espandi tutto Riduci tutto SCUOLA INTERNAZIONALE SUPERIORE DI STUDI AVANZATI DI TRIESTE Italia Contributo UE € 124 408,70 Indirizzo VIA BONOMEA 265 34136 Trieste Mostra sulla mappa Regione Nord-Est Friuli-Venezia Giulia Trieste Tipo di attività Higher or Secondary Education Establishments Ricercatore principale Jacopo Stoppa (Dr.) Contatto amministrativo Gabriele Rizzetto (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato UNIVERSITA DEGLI STUDI DI PAVIA Italia Contributo UE € 387 527,30 Indirizzo STRADA NUOVA 65 27100 Pavia Mostra sulla mappa Regione Nord-Ovest Lombardia Pavia Tipo di attività Higher or Secondary Education Establishments Contatto amministrativo Sofia Baggini (Dr.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato
