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Project Information

MIRROR SYMMETRY AND RELATED TOPICS

Agency:
NSF

National Science Foundation

Project Number:
1601907
Contact PI / Project Leader:
BORISOV, LEV A
Awardee Organization:
RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK

Description

Abstract Text:
This research project concerns algebraic geometry, a branch of mathematics that studies the structure of the solutions of systems of polynomial equations. In the last twenty years, the pace of development of algebraic geometry has accelerated due to its mutually beneficial connections with mathematical physics, more specifically to string theory. The first two parts of this project aim to contribute to this growing area of research by verifying some of the mathematical predictions that are inspired by string theory. A third part of the project is expected to involve research by undergraduate students. In addition to its intrinsic scientific value in algebraic geometry, this part of the project is aimed at expanding the opportunities for undergraduate students to participate in cutting-edge mathematical research in a way that makes them cognizant of deep connections between different areas of mathematics. This project focuses on the double mirror phenomenon in algebraic geometry as well as some combinatorial aspects of the Eisenbud-Goto conjecture. The research involves three main directions of study. The first part of the project will further investigate the Pfaffian-Grassmannian double mirror example, with the goal of transferring ideas and techniques developed in the context of Calabi-Yau complete intersections in toric varieties to this new, more sophisticated setting. The second part of the project continues research in the direction of the Kawamata's conjecture, which states that birational Calabi-Yau varieties are derived equivalent. This is a fifteen-year-old conjecture of key importance to the area of homological mirror symmetry. The third part of the project tackles the longstanding Eisenbud-Goto conjecture in the particular case of toric varieties, which can be reformulated as a question about the structure of the sets of integer points in certain integer polytopes.
Project Terms:
15 year old; Algebraic Geometry; Area; combinatorial; Development; Equation; Goals; Mathematics; Physics; Polynomial Models; Research; Research Project Grants; string theory; Structure; System; Techniques; undergraduate student

Details

Contact PI / Project Leader Information:
Name:  BORISOV, LEV A
Other PI Information:
Not Applicable
Awardee Organization:
Name:  RUTGERS THE ST UNIV OF NJ NEW BRUNSWICK
City:  PISCATAWAY    
Country:  UNITED STATES
Congressional District:
State Code:  NJ
District:  06
Other Information:
Fiscal Year: 2016
Award Notice Date: 18-Aug-2016
DUNS Number: 001912864
Project Start Date: 01-Sep-2016
Budget Start Date:
CFDA Code: 47.049
Project End Date: 31-Aug-2019
Budget End Date:
Agency: ?

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National Science Foundation
Project Funding Information for 2016:
Year Agency

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FY Total Cost
2016 NSF

National Science Foundation

$154,000

Results

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