| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | February 7, 2018 |
| Latest Amendment Date: | April 28, 2025 |
| Award Number: | 1749013 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Swatee Naik
snaik@nsf.gov (703)292-4876 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | June 1, 2018 |
| End Date: | May 31, 2026 (Estimated) |
| Total Intended Award Amount: | $400,000.00 |
| Total Awarded Amount to Date: | $400,000.00 |
| Funds Obligated to Date: |
FY 2019 = $81,902.00 FY 2020 = $83,842.00 FY 2021 = $85,866.00 FY 2022 = $87,978.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
809 S MARSHFIELD AVE M/C 551 CHICAGO IL US 60612-4305 (312)996-2862 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Chicago IL US 60607-7045 |
| 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): |
TOPOLOGY, GEOMETRIC ANALYSIS, Division Co-Funding: CAREER |
| Primary Program Source: |
01002021DB NSF RESEARCH & RELATED ACTIVIT 01002122DB NSF RESEARCH & RELATED ACTIVIT 01001920DB NSF RESEARCH & RELATED ACTIVIT 01001819DB 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
This National Science Foundation CAREER award supports research in an area of mathematics that provides powerful tools to tackle problems in geometry and mathematical physics. Building on her successful NSF-funded research, the PI will work with topological objects known as Higgs bundles, and their corresponding spaces of flat connections. The driving themes for the educational component of the project are inclusion of underrepresented groups, building a community of researchers in the USA, and outreach to K-12. The PI will organize several yearly workshops aimed at graduate students and young researchers, with attention paid to welcoming minorities.
The PI, together with her collaborators, will undertake research towards understanding the appearance of Lagrangian submanifolds of the moduli space of Higgs bundles supporting holomorphic sheaves (A-branes) and their dual spaces (B-branes). The overarching goal of the project is to obtain a geometric classification and to perform a thorough study of branes in the derived category of coherent sheaves and the Fukaya category of the moduli spaces of Higgs bundles, to extend the novel methods to other hyperkahler spaces, and to understand their implications for the geometric Langlands program. To this aim, the PI shall develop new tools to construct naturally arising families of branes not only within flat connections and Higgs bundles, but also in other hyperkahler settings. Moreover, the PI shall explore different geometric structures appearing through branes, including the study of hyperpolygons and automorphism groups, and further nonabelianization of spaces.
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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