| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | March 5, 2019 |
| Latest Amendment Date: | March 5, 2019 |
| Award Number: | 1902921 |
| Award Instrument: | Fellowship Award |
| Program Manager: |
Stefaan De Winter
sgdewint@nsf.gov (703)292-2599 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 1, 2019 |
| End Date: | June 30, 2023 (Estimated) |
| Total Intended Award Amount: | $150,000.00 |
| Total Awarded Amount to Date: | $150,000.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
Chicago IL US 60637-1514 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Cambridge MA US 02138-2901 |
| 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): | Workforce (MSPRF) MathSciPDFel |
| 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 award is made as part of the FY 2019 Mathematical Sciences Postdoctoral Research Fellowships Program. Each of the fellowships supports a research and training project at a host institution in the mathematical sciences, including applications to other disciplines, under the mentorship of a sponsoring scientist. The title of the project for this fellowship to Ana S. Balibanu is "Geometric Structures in Representation Theory". The host institution for the fellowship is Harvard University and the sponsoring scientist is Dennis Gaitsgory.
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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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
This work supported by this project centers on geometric representation theory, which is the study of symmetries of geometric objects. These symmetries form groups, and the interplay between the algebraic behavior of these groups and the geometric features of the underlying spaces can be leveraged to give new insights into both.
The work supported by this project laid the groundwork for an ongoing program to use geometric representation theory to gain a new understanding of Poisson geometry, which is a broad generalization of Hamiltonian mechanics. While supported by this award, the PI introduced several new representation-theoretic Poisson varieties, including relative compactifications of the additive and multiplicative universal centralizers.
In a parallel family of projects, the PI leveraged this perspective to study Hessenberg varieties, which are important objects in algebraic combinatorics. By viewing them as fibers of a degenerating family, the PI characterized their geometry and proved a novel connection between these spaces and the wonderful compactification.
While supported by this award, the PI gave over twenty research talks, including two expository minicourses on questions related to her research program. She also founded and ran a very popular general audience undergraduate colloquium series in her department, she organized two conferences, she mentored several graduate students, and she served on a substantial number of departmental committees.
Last Modified: 12/12/2023
Modified by: Ana S Balibanu
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