NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	UNIVERSITY OF ILLINOIS
Initial Amendment Date:	July 27, 2001
Latest Amendment Date:	June 26, 2002
Award Number:	0104150
Award Instrument:	Continuing Grant
Program Manager:	Alexandre Freire DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	August 1, 2001
End Date:	July 31, 2004 (Estimated)
Total Intended Award Amount:	$59,003.00
Total Awarded Amount to Date:	$59,003.00
Funds Obligated to Date:	FY 2001 = $30,304.00 FY 2002 = $28,699.00
History of Investigator:	Wei-Dong Ruan (Principal Investigator) ruan@math.uic.edu
Recipient Sponsored Research Office:	University of Illinois at Chicago 809 S MARSHFIELD AVE M/C 551 CHICAGO IL  US  60612-4305 (312)996-2862
Sponsor Congressional District:	07
Primary Place of Performance:	University of Illinois at Chicago 809 S MARSHFIELD AVE M/C 551 CHICAGO IL  US  60612-4305
Primary Place of Performance Congressional District:	07
Unique Entity Identifier (UEI):	W8XEAJDKMXH3
Parent UEI:
NSF Program(s):	GEOMETRIC ANALYSIS
Primary Program Source:	01000102DB NSF RESEARCH & RELATED ACTIVIT app-0102
Program Reference Code(s):	0000, OTHR
Program Element Code(s):	126500
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

Abstract for DMS - 0104150
PI: Wei-Dong Ruan

Dr. Ruan proposes to study the Lagrangian fibration structure of
Calabi-Yau manifolds and of more general Kaehler manifolds,
and their applications in mirror symmetry
and other Kahler geometry problems as well. The objective of the proposed research
is to further inderstand the Lagrangian torus fibration structures for more
general Calabi-Yau manifolds, exploring the interplay of sympletic
geometry and complex geometry in Kaehler manifolds, as indicated
by Kontsevich's categorical mirror symmetry program.

Mirror symmetry has its origin in string theory and
says that we have two theories, which appear to be completely distinct,
describing the same physics. If we have two different models of the same universe,
one can expect that one of the models can fill in the gaps in understanding
the other model. This project is towards understanding this symmetry principle.
Results from this proposal should be of interest to mathematicians from
various disciplines as well as physicists in string theory.

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