Obiettivo Very recently Dr. Julius Ross at the Univ. of Cambridge and I found a striking connection between geodesic rays in spaces of Kähler metrics and the Hele-Shaw flow (Laplacian growth). By this connection both have a similar interpretation as certain families of embedded holomorphic curves attached along their boundaries to a Lagrangian submanifold.The first objective is to develop the regularity theory of the Hele-Shaw flow (Laplacian growth) using techniques from the theory of moduli spaces of embedded holomorphic curves. These are powerful techniques used with great success in e.g. Gromov-Witten Theory and various Floer theories in symplectic topology. I thus hope to extend the short-time regularity result of Kufarev and Vinogradov, and also gain new insights as to how and when singularities occur.The second objective is to develop the regularity theory for (weak) geodesic rays in spaces of (cohomologically equivalent) Kähler metrics, using the Hele-Shaw flow as a one (complex) dimensional model case. Donaldson, and later Chen and Tian, have successfully applied techniques from the theory of moduli spaces of embedded holomorphic curves to a related problem connected to the regularity of geodesic segments rather than rays. Dr. Ross and I have a preliminary method to adapt some of these techniques to the setting of geodesic rays. Campo scientifico natural sciencesmathematicspure mathematicstopologysymplectic topology Programma(i) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Argomento(i) FP7-PEOPLE-2012-IEF - Marie-Curie Action: "Intra-European fellowships for career development" Invito a presentare proposte FP7-PEOPLE-2012-IEF Vedi altri progetti per questo bando Meccanismo di finanziamento MC-IEF - Intra-European Fellowships (IEF) Coordinatore THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE Contributo UE € 231 283,20 Indirizzo TRINITY LANE THE OLD SCHOOLS CB2 1TN Cambridge Regno Unito Mostra sulla mappa Regione East of England East Anglia Cambridgeshire CC Tipo di attività Higher or Secondary Education Establishments Contatto amministrativo Renata Schaeffer (Ms.) Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Costo totale Nessun dato
