NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	THE JOHNS HOPKINS UNIVERSITY
Initial Amendment Date:	April 3, 2013
Latest Amendment Date:	April 3, 2013
Award Number:	1300867
Award Instrument:	Continuing Grant
Program Manager:	Bruce P. Palka DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	July 1, 2013
End Date:	December 31, 2013 (Estimated)
Total Intended Award Amount:	$127,000.00
Total Awarded Amount to Date:	$41,690.00
Funds Obligated to Date:	FY 2013 = $0.00
History of Investigator:	Yuan Yuan (Principal Investigator) yyuan05@syr.edu
Recipient Sponsored Research Office:	Johns Hopkins University 3400 N CHARLES ST BALTIMORE MD  US  21218-2608 (443)997-1898
Sponsor Congressional District:	07
Primary Place of Performance:	Johns Hopkins University 3400 N Charles Street Baltimore MD  US  21218-2682
Primary Place of Performance Congressional District:	07
Unique Entity Identifier (UEI):	FTMTDMBR29C7
Parent UEI:	GS4PNKTRNKL3
NSF Program(s):	ANALYSIS PROGRAM
Primary Program Source:	01001314DB NSF RESEARCH & RELATED ACTIVIT 01001415DB NSF RESEARCH & RELATED ACTIVIT 01001516DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s):
Program Element Code(s):	128100
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

This mathematics research project by Yuan Yuan concerns a number of problems in several complex variables and complex differential geometry, consisting of the rigidity and classification of holomorphic structures, canonical metrics in Kahler geometry, and complex Monge-Ampere equations. These are fundamental problems closely related to many other fields in mathematics and physics, such as, algebraic geometry, mathematical physics, number theory, partial differential equations. In particular, Yuan will study the uniqueness of complex structure on Hermitian symmetric spaces and mapping rigidity between bounded symmetric domains; and the deep relation between the (finite and infinite time) limit behavior of the (parabolic) complex Monge-Ampere equations and canonical Kahler metrics as well as the formation of singularities on Kahler manifolds.

The mathematics field of complex analysis took center stage starting with the nineteenth century, when its applications became crucial to other sciences and engineering, including electronic engineering and mechanic engineering. Over the years, this trend has continued and in fact has been taken to the next level: the geometric spaces studied in this mathematics research project by Yuan Yuan can serve as the most basic models in cosmology and general relativity. Clarifying the geometric structure of these models is extremely important in understanding the physical laws that relate to them and can help further our understanding of the shape of the universe. In addition to this work, Yuan will continue to participate in, and organize seminars and workshops for undergraduate and graduate students and young researchers. Yuan will also mentor undergraduate and graduate students, and in this way the project will effectively integrate research and education.

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