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CFUC

Calabi flows with unbounded curvature

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EC-Contrib. €

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Partnership

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 CFUC project word cloud

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Project "CFUC" data sheet

The following table provides information about the project.

Coordinator
THE UNIVERSITY OF WARWICK 

Organization address
address: Kirby Corner Road - University House
city: COVENTRY
postcode: CV4 8UW
website: www.warwick.ac.uk

contact info
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surname: n.a.
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 Coordinator Country United Kingdom [UK]
 Project website https://sites.google.com/site/drkaizheng/home
 Total cost 183˙454 €
 EC max contribution 183˙454 € (100%)
 Programme 1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
 Code Call H2020-MSCA-IF-2015
 Funding Scheme MSCA-IF-EF-ST
 Starting year 2016
 Duration (year-month-day) from 2016-05-26   to  2018-05-25

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    THE UNIVERSITY OF WARWICK UK (COVENTRY) coordinator 183˙454.00

Map

 Project objective

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.

 Publications

year authors and title journal last update
List of publications.
2018 Li, Long; Wang, Jian; Zheng, Kai
Conic singularities metrics with prescribed scalar curvature: a priori estimates for normal crossing divisors
published pages: , ISSN: , DOI:
2019-06-13
2016 Yin, Hao; Zheng, Kai
Expansion formula for complex Monge-Amp`ere equation along cone singularities
published pages: , ISSN: , DOI:
2019-06-13
2018 Julien Keller, Kai Zheng
Construction of constant scalar curvature Kähler cone metrics
published pages: 527-573, ISSN: 0024-6115, DOI: 10.1112/plms.12132
Proceedings of the London Mathematical Society 117/3 2019-06-13
2017 Long Li, Kai Zheng
Uniqueness of constant scalar curvature Kähler metrics with cone singularities. I: reductivity
published pages: , ISSN: 0025-5831, DOI: 10.1007/s00208-017-1626-z
Mathematische Annalen 2019-06-13
2018 Haozhao Li, Bing Wang, Kai Zheng
Regularity Scales and Convergence of the Calabi Flow
published pages: 2050-2101, ISSN: 1050-6926, DOI: 10.1007/s12220-017-9896-y
The Journal of Geometric Analysis 28/3 2019-06-13
2018 Zheng, Kai
Existence of constant scalar curvature Kaehler cone metrics, properness and geodesic stability
published pages: , ISSN: , DOI:
2019-06-13
2018 Long Li, Kai Zheng
Generalized Matsushima’s theorem and Kähler–Einstein cone metrics
published pages: , ISSN: 0944-2669, DOI: 10.1007/s00526-018-1313-2
Calculus of Variations and Partial Differential Equations 57/2 2019-06-13
2018 Zheng, Kai
Geodesics in the space of Kahler cone metrics, II. Uniqueness of constant scalar curvature Kahler cone metrics
published pages: , ISSN: 0010-3640, DOI:
Communications on Pure and Applied Mathematics 2019-06-13
2016 Calamai, Simone; Petrecca, David; Zheng, Kai
On the geodesic problem for the Dirichlet metric and the Ebin metric on the space of Sasakian metrics.
published pages: 1111-1133, ISSN: 1076-9803, DOI:
New York Journal of Mathematics Volume 22 2019-06-13

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