| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | April 2, 2014 |
| Latest Amendment Date: | April 2, 2014 |
| Award Number: | 1401123 |
| Award Instrument: | Fellowship Award |
| Program Manager: |
Victor Roytburd
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 1, 2014 |
| End Date: | August 31, 2018 (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: |
Hayward CA US 94544-6674 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
CA US 94305-4020 |
| 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 IN THE MATHEMAT SCI |
| 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 2014 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 Nike Sun is "Probability Theory and Statistical Physics." The host institution for the fellowship is the Massachusetts Institute of Technology, and the sponsoring scientist is Dr. Scott Sheffield.
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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.
Much of this project concerned the asymptotic behavior of random constraint satisfaction problems (CSPs). The study of such problems is motivated in part by questions of computational complexity in average-case (or typical) scenarios, which go back at least to the 1980s. Statistical physicists have also extensively studied such problems from the point of view that they are similar to classical models of spin glasses or disordered magnets. Analytical heuristics developed by physicists suggest a wide range of interesting phenomena -- along with certain universal behaviors -- in the large-system limit for random CSPs and spin glasses (a broader class of related models). During this project we made progress in the rigorous mathematical understanding of such phenomena. In particular we developed (with collaborators Jian Ding, Allan Sly, and Yumeng Zhang) a rather detailed understanding of first-order behavior in the random regular NAE-SAT model, a simple model of boolean satisfiability. In this project we also proved the random k-SAT threshold conjecture for large k. In the course of these various works we also developed some new abstract techniques for computing moments of complicated spin systems: it is typically a difficult nonconvex optimization problem, but we have developed some general approaches to making such problems more tractable.
Last Modified: 12/03/2018
Modified by: Nike Sun
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