| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | July 9, 2024 |
| Latest Amendment Date: | July 9, 2024 |
| Award Number: | 2336788 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Elizabeth Wilmer
ewilmer@nsf.gov (703)292-7021 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: | $400,000.00 |
| Total Awarded Amount to Date: | $7,709.00 |
| Funds Obligated to Date: |
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| 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: |
809 S MARSHFIELD AVE M/C 551 CHICAGO IL US 60612-4305 |
| 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): | PROBABILITY |
| 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
This project focuses on the mathematical area of probability theory, the study of random structures. Random structures are ubiquitous throughout the sciences for their use as models as well as their use in the design of algorithms. The main focus of this project is on random structures in high dimensions, meaning random structures with many degrees of freedom. Some examples are random matrices, random sphere packings and random polynomials. Each of these classes of models has direct application in various other scientific fields such as data science, statistical physics and theoretical computer science. The project includes workshops for early-career researchers and graduate students, with an aim of bringing together disparate mathematical subfields.
The project consists of three components, with specific problems chosen with the aim of developing new techniques in high-dimensional probability and the use of analytic approaches in probability theory. The first component of the project concerns universality properties of random polynomials along with their use in optimization and algorithmic problems. The second component focuses on the structure of random sphere packings using connections to more combinatorial objects such as independent sets. The third component studies the non-asymptotic theory of random matrices with a focus on extremal behavior such as understanding the behavior of the least singular value in models without independent entries.
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.