| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | February 11, 2019 |
| Latest Amendment Date: | August 16, 2023 |
| Award Number: | 1844768 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
James Matthew Douglass
mdouglas@nsf.gov (703)292-2467 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 1, 2019 |
| End Date: | June 30, 2026 (Estimated) |
| Total Intended Award Amount: | $399,928.00 |
| Total Awarded Amount to Date: | $399,928.00 |
| Funds Obligated to Date: |
FY 2020 = $78,209.00 FY 2021 = $101,537.00 FY 2022 = $105,171.00 FY 2023 = $108,953.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
1 PROSPECT ST PROVIDENCE RI US 02912-9100 (401)863-2777 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
RI US 02912-9002 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): |
ALGEBRA,NUMBER THEORY,AND COM, Combinatorics |
| Primary Program Source: |
01002223DB NSF RESEARCH & RELATED ACTIVIT 01002122DB NSF RESEARCH & RELATED ACTIVIT 01001920DB NSF RESEARCH & RELATED ACTIVIT 01002324DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
Algebraic geometry is a central subject in mathematics and has connections and applications to many areas in mathematics, physics, and engineering. Algebraic geometers study spaces called algebraic varieties that are defined by polynomial equations. One powerful method of studying these spaces, as used in this project, is the method of degenerations, where a parametrized family of algebraic varieties breaks into pieces in the limit. Roughly speaking, the idea is that one studies the combinatorics, i.e. the discrete data, of the pieces, in order to deduce things about the more complicated original space. The educational component of the project includes a Women in Algebraic Geometry Workshop and a seminar series on diversity and inclusion in mathematics.
The research supported by this award will center on using modern degeneration techniques, especially those from the field of tropical geometry, to study classical spaces from algebraic geometry. In one direction, the PI will use these techniques to study the topology of classical moduli spaces of curves and abelian varieties. In another direction, the PI will also advance our understanding of Brill-Noether varieties using the combinatorics of set-valued tableaux, and investigate questions in tableau combinatorics that were motivated by the program in Brill-Noether theory. This award will also support a Women in Algebraic Geometry workshop and a seminar series on diversity and inclusion in mathematics.
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.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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