| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | December 9, 2016 |
| Latest Amendment Date: | December 9, 2016 |
| Award Number: | 1656377 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Tomek Bartoszynski
tbartosz@nsf.gov (703)292-4885 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | January 1, 2017 |
| End Date: | December 31, 2017 (Estimated) |
| Total Intended Award Amount: | $49,450.00 |
| Total Awarded Amount to Date: | $49,450.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
201 PRESIDENTS CIR SALT LAKE CITY UT US 84112-9049 (801)581-6903 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
UT US 84112-8930 |
| 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: |
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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
The Semester on KPZ Universality and Directed Polymers will be hosted at the Centre International de Rencontres Mathematiques, in Luminy, France, from February 1 to July 31, 2017. The purpose of the programme is to bring together leading researchers from around the world to strengthen our understanding of KPZ universality. This is one of the most active areas of statistical mechanics and mathematical physics in the last ten years that is focused on studying the extremes of highly correlated random systems. Remarkably, the statistics governing the extremes appear to be universal regardless of the particular system under consideration, although thus far this has only been understood for very specific systems. The main focus of the program is to understand the unifying mechanism behind the universality, motivated by examples from directed polymer models. This will be done in an interdisciplinary manner using ideas from statistical mechanics, probability theory, dynamical systems, and partial differential equations. The intellectual merit of the semester lies in its potential to establish a cross-fertilization of ideas within different areas of mathematics and connect these ideas with theoretical physics and other fields of science. Broader impact will be realized via this exchange of ideas across disciplines and through the training of a new generation of students to carry on the work in this important field.
In addition to enabling long-term collaborations between leading researchers, the semester will allow for the dissemination of new results with a conference on Qualitative Methods in KPZ Universality (April 24-27, 2017) and a small groups meeting on Random Walks in Random Environments (March 13-17, 2017).There will also be a research school on Random Structures in Statistical Mechanics and Mathematical Physics (March 6-10, 2017) aimed at introducing graduate students and other junior researchers to this exciting new field. Funds from this proposal will enable the participation of United States based students and junior researchers in these programs.
Conference website: khanin-shlosman.weebly.com
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.
The semester on KPZ Universality and Directed Polymers was held at the Centre International de Recontres Mathematiques from January - July 2017 to create a new, state-of-the-art level of research in this exciting field. Since the discovery of the Tracy-Widom distribution in 1994 the universality of Kardar-Parisi-Zhang (KPZ) scalings has become one of the most active areas of probability theory, statistical mechanics, and mathematical physics. The mathematical theory behind it is rich and complex, especially in connection with directed polymer problems, and there are new problems emerging regularly with connections to disciplines as diverse as crystal growth and wireless communications.
The central ambition of the semester was to bring together mathematicians with different specialties in order to develop and establish qualitative methods for KPZ universality that are applicable in very general situations. Success in this objective relied crucially on the interdisciplinary nature of the semester and required ideas coming from probability theory, operator analysis, mathematical physics, combinatorics, dynamical systems, partial differential equations, and stochastic analysis. The semester was remarkable for its level of interest from both mathematicians and theoretical physicists, and the far reaching applications it showed in both areas.
The scientific programme consisted of a conference on Qualitative Methods in KPZ Universality, a small group workshop on Random Walks in Random Environments, and Research in Pairs events on the Ising Model and Weak Universality for the KPZ Equation. The main conference was attended by over 50 participants, and several new and exciting results were discussed during this time. Several new collaborations were born from the main conference, leading to new ideas and eventual publication in top journals. Preprints are being maintained on the semester website at khanin-shlosman.weebly.com
The semester also had an important educational component that greatly benefited young researchers. The semester began with an intensive, weak long research school on Random Structures in Statistical Mechanics and Mathematical Physics. Six leading researchers gave a series of introductory lectures on the most recent developments in the field, which allowed young researchers to learn about the subject in a focused and unified way. This lead to a degree of interconnectedness between researchers that was cited as a key benefit of the research school. The school was attended by nearly 40 participants, 13 of whom were young researchers supported by the funds from this grant.
The present NSF funding was used to allow young researchers from US universities to attend the semester and partake in its activities. This provided these researchers with a tremendous opportunity to branch out into new research fields and collaborate with scientists that they would not normally interact with. Particular effort was made to recruit younger women and minorities to the programme. The participation of these researchers will greatly further their education and train them to continue in this line of research for years to come.
Last Modified: 02/18/2018
Modified by: Thomas K Alberts
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