Obiettivo In the 1950s, Calabi proposed a program in Kahler geometry and then introduced the Calabi flow, aiming to find the constant scalar curvature Kahler (cscK) metrics. When the first Chern class is zero, the cscK metric reduces to Ricci flat Kahler metric. The problem to find such metrics is called Calabi conjecture. Its resolution was Yau's Fields medal work. Generally, it is known as the Yau-Tian-Donaldson conjecture. Geometric flow provides an effective way to find canonical metrics. E.g. the theory by Hamilton and Perelman of Ricci flow has achieved great success to solve the conjecture of Poincare and Thurston, one of the seven $1 million Clay Mathematics Institute Millennium Prizes. X.X. Chen conjectured the Calab flow has long time existence. This proposal concerns singularity analysis of the Calabi flow, when the curvature gets unbounded. Warwick leads a major new project funded by an EPSRC grant 'Singularities of Geometric PDEs', together with Imperial and Cambridge, making it a natural host for this proposal. The supervisor Topping is the Principal investigator of this project. He is a leading expert on geometric flows and nonlinear PDEs. He has considerable experience in supervising research: 14 postdocs and 8 PhD students. Currently, he is working on Ricci flows with unbounded curvature and presented an invited 45-minute lecture on this topic at Seoul ICM in 2014.Zheng completed his PhD at the Chinese Academic of Sciences under the supervision of W.Y. Ding and X.X. Chen. From his advisors, Zheng gained intimate understanding of Kahler geometry. He worked as a postdoc at the Institut Fourier in France and then Leibniz Universitaet in Germany. Up to May 2015, his research experience has entirely been outside UK. He is ambitious to establish himself as an independent researcher at a prestigious UK institution. He has published 8 papers in high reputation international journals. This project will help him to integrate himself into the UK research system. Campo scientifico natural sciencescomputer and information sciencesnatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsmathematical analysisdifferential equationspartial differential equationsnatural sciencesmathematicspure mathematicsalgebraalgebraic geometry Programma(i) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Argomento(i) MSCA-IF-2015-EF - Marie Skłodowska-Curie Individual Fellowships (IF-EF) Invito a presentare proposte H2020-MSCA-IF-2015 Vedi altri progetti per questo bando Meccanismo di finanziamento MSCA-IF-EF-ST - Standard EF Coordinatore UNIVERSITY OF WARWICK Contribution nette de l'UE € 183 454,80 Indirizzo KIRBY CORNER ROAD UNIVERSITY HOUSE CV4 8UW COVENTRY Regno Unito Mostra sulla mappa Regione West Midlands (England) West Midlands Coventry Tipo di attività Higher or Secondary Education Establishments Collegamenti Contatta l’organizzazione Opens in new window Sito web Opens in new window Partecipazione a programmi di R&I dell'UE Opens in new window Rete di collaborazione HORIZON Opens in new window Costo totale € 183 454,80