Cel 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. Dziedzina nauki natural sciencesmathematicspure mathematicstopologysymplectic topology Program(-y) FP7-PEOPLE - Specific programme "People" implementing the Seventh Framework Programme of the European Community for research, technological development and demonstration activities (2007 to 2013) Temat(-y) FP7-PEOPLE-2012-IEF - Marie-Curie Action: "Intra-European fellowships for career development" Zaproszenie do składania wniosków FP7-PEOPLE-2012-IEF Zobacz inne projekty w ramach tego zaproszenia System finansowania MC-IEF - Intra-European Fellowships (IEF) Koordynator THE CHANCELLOR MASTERS AND SCHOLARS OF THE UNIVERSITY OF CAMBRIDGE Wkład UE € 231 283,20 Adres TRINITY LANE THE OLD SCHOOLS CB2 1TN Cambridge Zjednoczone Królestwo Zobacz na mapie Region East of England East Anglia Cambridgeshire CC Rodzaj działalności Higher or Secondary Education Establishments Kontakt administracyjny Renata Schaeffer (Ms.) Linki Kontakt z organizacją Opens in new window Strona internetowa Opens in new window Koszt całkowity Brak danych