| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | June 15, 2004 |
| Latest Amendment Date: | June 12, 2006 |
| Award Number: | 0354962 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Joe W. Jenkins
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 1, 2004 |
| End Date: | June 30, 2007 (Estimated) |
| Total Intended Award Amount: | $141,000.00 |
| Total Awarded Amount to Date: | $141,000.00 |
| Funds Obligated to Date: |
FY 2005 = $47,000.00 FY 2006 = $47,000.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
107 S INDIANA AVE BLOOMINGTON IN US 47405-7000 (317)278-3473 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
107 S INDIANA AVE BLOOMINGTON IN US 47405-7000 |
| 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): | ANALYSIS PROGRAM |
| Primary Program Source: |
app-0105 app-0106 |
| 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
ABSTRACT
Bleher
This research project is directed on fundamental problems of the
theory of random matrices and random polynomials and their
applications, and on related problems in statistical physics. The
cornerstone of the problems is different conjectures of universality,
which state that as the size of a random matrix (or the degree of a
random polynomial) approaches infinity, the correlations between
properly scaled eigenvalues (or zeros) approach a universal limit. In
the current project the PI continues his studies of the universality
in random matrix models, random polynomials, and statistical
physics. This includes: (i) The Riemann-Hilbert (RH) approach to
double scaling limits in random matrix models. (ii) RH approach to
random matrices with external source. (iii) Semiclassical asymptotics
and RH approach to multi-matrix models. (iv) RH approach to the
six-vertex model of statistical physics. (v) Scaling limits and
universality in non-Gaussian ensembles of random polynomials and
random algebraic varieties.
The project has an interdisciplinary character and it lies on the
frontier between physics and mathematics. The problems of scaling and
universality are central in many areas of modern science: theory of
critical phenomena and phase transitions, statistical physics and
quantum field theory, theory of quantum chaos, nonlinear dynamics,
etc. This project is directed on development of powerful mathematical
methods to the problems of scaling and universality in the theory of
random matrices, random polynomials, and related topics. It involves
different areas of mathematics: analysis, theory of integrable
systems, probability theory, semiclassical asymptotics for systems of
differential equations, complex analysis, etc. The research project
under consideration has direct applications to various physical
problems: combinatorial asymptotics related to quantum gravity,
exactly solvable models of statistical physics, spin systems on random
surfaces, theory of critical phenomena and phase transitions, quantum
chaos. Possible further applications include theory of knots and
links and related problems in molecular biology, growth models,
statistical data analysis, and others.
Please report errors in award information by writing to: awardsearch@nsf.gov.
