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Project Information

CANONICAL METRICS, GEOMETRIC FLOWS AND FORMATION OF SINGULARITIES

Agency:
NSF

National Science Foundation

Project Number:
1406124
Contact PI / Project Leader:
SONG, JIAN
Awardee Organization:
RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK

Description

Abstract Text:
Recent progress and influx of new ideas have unraveled a deep, rich and unifying structure among analysis, Riemannian geometry, pluripotential theory, classical several complex variables and the minimal model program in algebraic geometry. The proposed research work focuses on a number of open problems and developing programs on canonical metrics, geometric flows and complex Monge-Ampere equations arising from geometry and physics. The proposed project also aims to bring in research and teaching innovation in mathematics from various disciplines and have an immediate beneficial effect on graduate and undergraduate students at Rutgers as well as in the regional community of mathematics. The PI will also organize and participate in the integrated research/education programs and activities that will promote the education level of the nation. Furthermore, the PI plans to disseminate the exciting frontier research at the interface of geometry, analysis and algebra to a broad audience through lectures and survey papers.

The PI will investigate and continue to make progress in the analytic minimal model program with Ricci flow. In particular, the PI will study both the finite time and long time formation of singularities of the Kahler-Ricci flow on algebraic varieties. Such singularity formation is reflected by canonical geometric/analytic surgeries equivalent to birational transformations and should be understood through global and local metric uniformization. The PI will also investigate the canonical metrics of Einstein type on singular varieties, in particular, the Riemannian geometric properties of such singular metrics and related moduli problems with applications in string theory such as geometric transitions and mirror symmetry. The PI willy employ new theories and techniques from L^2-theory, nonlinear PDEs, Perelman's works and Cheeger-Colding theory. The outcome of the proposed research will develop new tools and give profound insights of the structure of the universe as well as many other applied sciences.
Project Terms:
Algebra; Algebraic Geometry; Applied Research; Communities; Complex; Complex Variables; Discipline; Education; Educational Background; Educational process of instructing; Equation; frontier; Geometry; innovation; insight; lectures; Mathematics; Metric; Modeling; Operative Surgical Procedures; Outcome; Paper; Physics; programs; Property; Research; Structure; Surveys; Techniques; theories; Time; tool; undergraduate student; Work

Details

Contact PI / Project Leader Information:
Name:  SONG, JIAN
Other PI Information:
Not Applicable
Awardee Organization:
Name:  RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK
City:  NEW BRUNSWICK    
Country:  UNITED STATES
Congressional District:
State Code:  NJ
District:  06
Other Information:
Fiscal Year: 2014
Award Notice Date: 03-Jul-2014
DUNS Number: 001912864
Project Start Date: 01-Aug-2014
Budget Start Date:
CFDA Code: 47.049
Project End Date: 31-Jul-2017
Budget End Date:
Agency: ?

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National Science Foundation
Project Funding Information for 2014:
Year Agency

Agency: The entity responsible for the administering of a research grant, project, or contract. This may represent a federal department, agency, or sub-agency (institute or center). Details on agencies in Federal RePORTER can be found in the FAQ page.

FY Total Cost
2014 NSF

National Science Foundation

$155,823

Results

i

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