NSF Org:	DMS Division Of Mathematical Sciences
Recipient:	THE TRUSTEES OF COLUMBIA UNIVERSITY IN THE CITY OF NEW YORK
Initial Amendment Date:	July 31, 2024
Latest Amendment Date:	July 31, 2024
Award Number:	2404945
Award Instrument:	Standard Grant
Program Manager:	Qun Li qli@nsf.gov  (703)292-7465 DMS  Division Of Mathematical Sciences MPS  Directorate for Mathematical and Physical Sciences
Start Date:	September 1, 2024
End Date:	August 31, 2027 (Estimated)
Total Intended Award Amount:	$219,328.00
Total Awarded Amount to Date:	$219,328.00
Funds Obligated to Date:	FY 2024 = $219,328.00
History of Investigator:	Mu-Tao Wang (Principal Investigator) mtwang@math.columbia.edu
Recipient Sponsored Research Office:	Columbia University 615 W 131ST ST NEW YORK NY  US  10027-7922 (212)854-6851
Sponsor Congressional District:	13
Primary Place of Performance:	Columbia University 2990 Broadway, RM 514 NEW YORK NY  US  10027-6902
Primary Place of Performance Congressional District:	13
Unique Entity Identifier (UEI):	F4N1QNPB95M4
Parent UEI:
NSF Program(s):	GEOMETRIC ANALYSIS
Primary Program Source:	01002425DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s):
Program Element Code(s):	126500
Award Agency Code:	4900
Fund Agency Code:	4900
Assistance Listing Number(s):	47.049

ABSTRACT

This project utilizes powerful geometric concepts, known as classical surface theories, to unlock the mysteries of spacetime. This research will deepen our understanding of gravity, black holes, and the very fabric of spacetime. The project's findings can complement experimental data on phenomena like gravitational waves, currently heavily reliant on numerical simulations. Novel methods developed during this research might find applications in other areas of mathematics and physics. The research in this project will also promote interests in mathematics among undergraduate and graduate students and young researchers in the mathematical community.

This project leverages the power of classical surface theories, including techniques like isometric embedding and the Gauss map, to investigate complex problems in differential geometry and general relativity. By focusing on the non-linear nature of spacetime, the research aims to:1.Evaluate the quasi-local mass of binary black holes: Develop a more precise method for calculating the combined mass and individual masses of these fascinating objects.2.Define angular momentum in general relativity: Establish a rigorous definition of angular momentum applicable to global solutions of Einstein's equations.3.Prove existence and regularity of a geometric flow: Mathematically demonstrate the existence and well-behaved nature of a specific type of geometric evolution. 4. Demonstrate duality in string theory: Reveal an underlying connection between two seemingly disparate equations within string theory, potentially leading to new avenues of exploration. These advancements promise to significantly contribute to our understanding of the universe and the power of mathematics in unraveling its mysteries.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

Please report errors in award information by writing to: awardsearch@nsf.gov.