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Program Search
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Upcoming Programs: |
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| Random Matrix Theory, Interacting Particle Systems and Integrable Systems |
| August 16, 2010 to December 17, 2010 |
| Organized By: Jinho Baik (University of Michigan), Alexei Borodin (California Institute of Technology), Percy A. Deift* (New York University, Courant Institute), Alice Guionnet (École Normale Supérieure de Lyon), Craig A. Tracy (University of California, Davis), and Pierre van Moerbeke, (Université Catholique de Louvain) |
| The goal of this program is to showcase the many remarkable developments that have taken place in the past decade in Random Matrix Theory (RMT) and to spur on further developments on RMT and the related areas Interacting Particle Systems (IPS) and Integrable Systems (IS): IPS provides an arena in which RMT behavior is frequently observed, and IS provides tools which are often useful in analyzing RMT and IPS/RMT behavior. |
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| Inverse Problems and Applications |
| August 16, 2010 to December 17, 2010 |
| Organized By: Liliana Borcea (Rice University), Maarten V. de Hoop (Purdue University), Carlos E. Kenig (University of Chicago), Peter Kuchment (Texas A&M University), Lassi Päivärinta (University of Helsinki), Gunther Uhlmann* (University of Washington), and Maciej Zworski (University of California, Berkeley) |
| Inverse Problems are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. Applications include a number of medical as
well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization,
model identification in growth processes and, more recently, modelling in the life sciences. During the last 10 years or so there has been significant developments both in the mathematical theory and applications of inverse problems. The purpose of the program would be to bring together people working on different aspects of the field, to appraise the current status of development and to encourage interaction between mathematicians and scientists and engineers working directly with the applications. |
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| Complementary Program 2010-11 |
| August 16, 2010 to May 20, 2011 |
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| Free Boundary Problems, Theory and Applications |
| January 10, 2011 to May 20, 2011 |
| Organized By: Luis Caffarelli (University of Texas), Henri Berestycki (Centre d’Analyse et de Mathèmatique Sociales), Laurence C. Evans (University of California), Mikhail Feldman (University of Wisconsin, Madison), John Ockendon (University of Oxford), Arshak Petrosyan (Purdue University), Henrik Shahgholian* (The Royal Institute of Technology), Tatiana Toro (University of Washington), and Nina Uraltseva (Steklov Mathematical Institute (POMI) |
| This program aims at the study of various topics within the area of Free Boundaries Problems, from the viewpoints of theory and applications. Many problems in physics, industry, finance, biology, and other areas can be described by partial differential equations that exhibit apriori unknown sets, such as interfaces, moving boundaries, shocks, etc. The study of such sets, also known as free boundaries, often occupies a central position in such problems. The aim of this program is to gather experts in the field with knowledge of various applied and theoretical aspects of free boundary problems. |
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| Arithmetic Statistics |
| January 10, 2011 to May 20, 2011 |
| Organized By: Brian Conrey (American Institute of Mathematics), John Cremona (University of Warwick), Barry Mazur (Harvard University), Michael Rubinstein* (University of Waterloo), Peter Sarnak (Princeton University), Nina Snaith (University of Bristol), and William Stein (University of Washington) |
| L -functions attached to modular forms and/or to algebraic varieties and algebraic number fields are prominent in quite a wide range of number theoretic issues, and our recent growth of understanding of the analytic properties of L-functions has already lead to profound applications regarding among other things the statistics related to arithmetic problems. This program will emphasize statistical aspects of L-functions, modular forms, and associated arithmetic and algebraic objects from several different perspectives — theoretical, algorithmic, and experimental. |
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| Quantitative Geometry |
| August 15, 2011 to December 16, 2011 |
| Organized By: Keith Ball (University College London), Emmanuel Breuillard (Universiè Paris-Sud 11, Orsay), Jeff Cheeger (New York University, Courant Institute), Marianna Csornyei (University College London), Mikhail Gromov (Courant Institute and Institut des Hautes Études Scientifiques), Bruce Kleiner (Yale University and Courant Institute), Vincent Lafforgue (Université Paris 6, Pierre et Marie Curie), Manor Mendel (The Open University of Israel), Assaf Naor* (New York University, Courant Institute), Yuval Peres (Microsoft Research Laboratories), and Terence Tao (University of California, Los Angeles) |
| The fall 2011 program "Quantitative Geometry" is devoted to the investigation of geometric questions in which quantitative/asymptotic considerations are inherent and necessary for the formulation of the problems being studied. Such topics arise naturally in a wide range of mathematical disciplines, with significant relevance both to the internal development of the respective fields, as well as to applications in areas such as theoretical computer science. Examples of areas that will be covered by the program are: geometric group theory, the theory of Lipschitz functions (e.g., Lipschitz extension problems and structural aspects such as quantitative differentiation), large scale and coarse geometry, embeddings of metric spaces and their applications to algorithm design, geometric aspects of harmonic analysis and probability, quantitative aspects of linear and non-linear Banach space theory, quantitative aspects of geometric measure theory and isoperimetry, and metric invariants arising from embedding theory and Riemannian geometry. The MSRI programs aims to crystallize the interactions between researchers in various relevant fields who might have a lack of common language, even though they are working on related questions. |
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| Random Spatial Processes |
| January 09, 2012 to May 18, 2012 |
| Organized By: Mireille Bousquet-Mélou (Université de Bordeaux), Richard Kenyon* (Brown University), Greg Lawler (University of Chicago), Andrei Okounkov (Princeton University), and Yuval Peres (Microsoft Research Laboratories) |
| In recent years probability theory (and here we mean probability theory in the largest sense, comprising combinatorics, statistical mechanics, algorithms, simulation) has made immense progress in understanding the basic two-dimensional models of statistical mechanics and random surfaces. Prior to the 1990’s the major interests and achievements of probability theory were (with some exceptions for dimensions 4 or more) with respect to one-dimensional objects: Brownian motion and stochastic processes, random trees, and the like. Inspired by work of physicists in the ’70s and ’80s on conformal invariance and field theories in two dimensions, a number of leading probabilists and combinatorialists began thinking about spatial process in two dimensions: percolation, polymers, dimer models, Ising models. Major breakthroughs by Kenyon, Schramm, Lawler, Werner, Smirnov, Sheffield, and others led to a rigorous underpinning of conformal invariance in two dimensional systems and paved the way for a new era of “two-dimensional” probability theory. |
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| Commutative Algebra |
| August 20, 2012 to May 24, 2013 |
| Organized By: David Eisenbud* (University of California, Berkeley), Srikanth Iyengar (University of Nebraska), Ezra Miller (Duke University), Anurag Singh (University of Utah), and Karen Smith (University of Michigan) |
| Commutative algebra was born in the 19th century from algebraic geometry, invariant theory, and number theory. Today it is a mature field with activity on many fronts, and important links to other areas such as algebraic topology, combinatorics, mathematical physics, noncommutative geometry, representation theory, singularity theory, and statistics. The program will reflect the wealth of interconnections suggested by these fields, and will introduce young researchers to these diverse areas.
One of the thrusts of the year-long program will be to foster new connections in addition to strengthening existing ones. The program will also highlight exciting recent developments in commutative algebra on syzygies and free resolutions, homological and representation theoretic aspects, tight closure and singularities, and birational geometry. |
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| Cluster Algebras |
| August 20, 2012 to December 21, 2012 |
| Organized By: Sergey Fomin (University of Michigan), Bernhard Keller (Universit´e Paris VII, France), Bernard Leclerc (Universit´e de Caen, France), Alexander Vainshtein* (University of Haifa, Israel), Lauren Williams (University of California, Berkeley). |
| Cluster algebras were conceived in the Spring of 2000
as a tool for studying dual canonical bases and total positivity in semisimple Lie
groups. They are constructively defined commutative algebras with a distinguished
set of generators (cluster variables) grouped into overlapping subsets (clusters) of
fixed cardinality. Both the generators and the relations among them are not given
from the outset, but are produced by an iterative process of successive mutations.
Although this procedure appears counter-intuitive at first, it turns out to encode
a surprisingly widespread range of phenomena, which might explain the explosive
development of the subject in recent years.
Cluster algebras provide a unifying
algebraic/combinatorial framework for a wide variety of phenomena in settings as
diverse as quiver representations, Teichm¨uller theory, invariant theory, tropical calculus,
Poisson geometry, Lie theory, and polyhedral combinatorics. |
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