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Minimize RSR Award Detail

Research Spending & Results

Award Detail

Awardee:TRUSTEES OF PRINCETON UNIVERSITY, THE
Doing Business As Name:Princeton University
PD/PI:
  • Kenneth B Ascher
  • (609) 258-6450
  • kascher@princeton.edu
Award Date:07/11/2020
Estimated Total Award Amount: $ 174,486
Funds Obligated to Date: $ 174,486
  • FY 2020=$174,486
Start Date:07/15/2020
End Date:06/30/2023
Transaction Type:Grant
Agency:NSF
Awarding Agency Code:4900
Funding Agency Code:4900
CFDA Number:47.049
Primary Program Source:040100 NSF RESEARCH & RELATED ACTIVIT
Award Title or Description:Higher Dimensional Algebraic Varieties: Geometry and Arithmetic
Federal Award ID Number:2001408
DUNS ID:002484665
Parent DUNS ID:002484665
Program:ALGEBRA,NUMBER THEORY,AND COM
Program Officer:
  • Michelle Manes
  • (703) 292-4870
  • mmanes@nsf.gov

Awardee Location

Street:Off. of Research & Proj. Admin.
City:Princeton
State:NJ
ZIP:08544-2020
County:Princeton
Country:US
Awardee Cong. District:12

Primary Place of Performance

Organization Name:Princeton University
Street:
City:Princeton
State:NJ
ZIP:08544-2020
County:Princeton
Country:US
Cong. District:12

Abstract at Time of Award

Algebraic geometry focuses on the study of solutions of polynomial equations. Guiding questions in this fields are to understand the geometric objects, called algebraic varieties, arising from polynomial equations and to classify such shapes. This project also concerns applications to number theory, with hopes to understand what the geometry of these shapes can tell us about the rational number or integral solutions to these polynomial equations. These problems have applications to other fields of math (e.g. differential geometry) as well as physics (e.g. string theory). Moduli spaces of higher dimensional algebraic varieties are not as well understood as their curve counterparts. The first overarching question in this project is to the understand compactifications of moduli spaces of higher dimensional algebraic varieties. The approaches taken will be a combination of techniques arising from, e.g. the minimal model program (MMP), as well as K-stability. In particular, the PI plans to understand explicit compactifications in specific cases (e.g. K3 surfaces), and to study how to interpolate between various compactifications in a modular way. The second overarching question, is to investigate how geometry of higher dimensional varieties and their moduli influences arithmetic, studying the rich interplay between algebraic geometry, hyperbolicity, and arithmetic geometry. 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.

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