| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | January 11, 2024 |
| Latest Amendment Date: | January 11, 2024 |
| Award Number: | 2338345 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Tim Hodges
thodges@nsf.gov (703)292-5359 DMS Division Of Mathematical Sciences MPS Direct For Mathematical & Physical Scien |
| Start Date: | September 1, 2024 |
| End Date: | August 31, 2029 (Estimated) |
| Total Intended Award Amount: | $549,455.00 |
| Total Awarded Amount to Date: | $113,376.00 |
| Funds Obligated to Date: |
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| 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: |
1 PROSPECT ST PROVIDENCE RI US 02912-9127 |
| 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 |
| Primary Program Source: |
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| 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
This project develops techniques to understand the geometry of the solutions to systems of polynomial equations. Of particular interest is when the set of solutions are one-dimensional, in which case it is called an algebraic curve. Since polynomials are ubiquitous in science and engineering, such solution sets arise in many different contexts. One important example is the interpolation problem: given a collection of general points, when is there a fixed type of algebraic curve passing through these points? This problem has applications to cryptography and information theory. The research projects will shed light on the possible realizations of an algebraic curve by polynomial equations, as well as new and important cases of the interpolation problem. This will be complemented by educational and outreach activities, including a sequence of workshops designed for early-to-mid career women and nonbinary graduate students in algebraic geometry and mentoring undergraduate research.
More specifically, the research projects are in the following three directions. The first focuses on the natural stratification of the space of vector bundles on a curve equipped with a fixed dominant map to another curve by the stability of the pushforward. The second focuses on the interpolation problem in other settings, including when the ambient variety is a homogeneous space. The last focuses on the rationality problem for varieties over nonclosed ground fields, and in particular upon generalizations of the intermediate Jacobian torsor obstruction.
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.
