| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | January 10, 2024 |
| Latest Amendment Date: | January 10, 2024 |
| Award Number: | 2340239 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Eriko Hironaka
ehironak@nsf.gov (703)292-7041 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | June 15, 2024 |
| End Date: | May 31, 2029 (Estimated) |
| Total Intended Award Amount: | $550,000.00 |
| Total Awarded Amount to Date: | $73,192.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
506 S WRIGHT ST URBANA IL US 61801-3620 (217)333-2187 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
506 S WRIGHT ST URBANA IL US 61801-3620 |
| 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 |
| Primary Program Source: |
01002526DB NSF RESEARCH & RELATED ACTIVIT 01002627DB NSF RESEARCH & RELATED ACTIVIT 01002728DB NSF RESEARCH & RELATED ACTIVIT 01002829DB 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
The research of this award lies at the interface between theoretical physics and geometry. An unsolved conjecture posits a deep connection between the geometry of supersymmetric quantum field theories and certain structures in algebraic topology. Resolving this conjecture would provide new insight into the mathematical foundations of quantum field theory, while also providing several long-anticipated applications of algebraic topology in physics. The projects the PI will work on leverage higher categorical symmetries to gain new insights into this 30-year-old conjecture. The award supports graduate students working with the PI whose research will contribute to this area. The PI will also continue his involvement in mathematics education for incarcerated people through the Education Justice Project in Illinois.
The proposed research is centered on an equivariant refinement of Stolz and Teichner?s conjectured geometric model for elliptic cohomology from 2-dimensional supersymmetric field theories. The overarching goal is to link structures in Lurie?s 2-equivariant elliptic cohomology with the geometry of supersymmetric gauge theories. Some of the projects are natural extensions of prior work at heights zero and one, focusing on height 2 generalizations of specific quantum field theories that are expected to construct elliptic Thom classes. Other projects will initiate the study of 2-equivariant geometry, interfacing with topics in string geometry, loop group representation theory, and elliptic power operations.
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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