
Program Mathematical General Relativity
Organizers: Yvonne ChoquetBruhat, Piotr Chrusciel (Universität Wien), Greg Galloway (University of Miami), Gerhard Huisken (Mathematisches Forschungsinstitut Oberwolfach), LEAD James Isenberg (University of Oregon), Sergiu Klainerman (Princeton University), Igor Rodnianski (Massachusetts Institute of Technology), Richard Schoen (Stanford University)The study of Einstein's general relativistic gravitational field equation, which has for many years played a crucial role in the modeling of physical cosmology and astrophysical phenomena, is increasingly a source for interesting and challenging problems in geometric analysis and PDE. In nonlinear hyperbolic PDE theory, the problem of determining if the Kerr black hole is stable has sparked a flurry of activity, leading to outstanding progress in the study of scattering and asymptotic behavior of solutions of wave equations on black hole backgrounds. The spectacular recent results of Christodoulou on trapped surface formation have likewise stimulated important advances in hyperbolic PDE. At the same time, the study of initial data for Einstein's equation has generated a wide variety of challenging problems in Riemannian geometry and elliptic PDE theory. These include issues, such as the Penrose inequality, related to the asymptotically defined mass of an astrophysical systems, as well as questions concerning the construction of non constant mean curvature solutions of the Einstein constraint equations. This semesterlong program aims to bring together researchers working in mathematical relativity, differential geometry, and PDE who wish to explore this rapidly growing area of mathematics.
Updated on Nov 05, 2013 04:41 PM PST 
Program Optimal Transport: Geometry and Dynamics
Organizers: Luigi Ambrosio (Scuola Normale Superiore), Yann Brenier (École Polytechnique), Panagiota Daskalopoulos (Columbia University), Lawrence Evans (University of California, Berkeley), Alessio Figalli (University of Texas), Wilfrid Gangbo (Georgia Institute of Technology), LEAD Robert McCann (University of Toronto), Felix Otto (MaxPlanckInstitut für Mathematik in den Naturwissenschaften), Neil Trudinger (Australian National University)In the past two decades, the theory of optimal transportation has emerged as a fertile field of inquiry, and a diverse tool for exploring applications within and beyond mathematics. This transformation occurred partly because longstanding issues could finally be resolved, but also because unexpected connections emerged which linked these questions to classical problems in geometry, partial differential equations, nonlinear dynamics, natural sciences, design problems and economics. The aim of this program will be to gather experts in optimal transport and areas of potential application to catalyze new investigations, disseminate progress, and invigorate ongoing exploration.
Updated on Sep 29, 2013 11:41 PM PDT 
Program Commutative Algebra
Organizers: 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.
The yearlong program will highlight exciting recent developments in core areas such as free resolutions, homological and representation theoretic aspects, Rees algebras and integral closure, tight closure and singularities, and birational geometry. In addition, it will feature the 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.
New connections will be fostered through collaboration with the concurrent MSRI programs in Cluster Algebras (Fall 2012) and Noncommutative Algebraic Geometry and Representation Theory (Spring 2013).
For more detailed information about the program please see, http://www.math.utah.edu/ca/.
Updated on Aug 18, 2013 04:09 PM PDT 
Program Noncommutative Algebraic Geometry and Representation Theory
Organizers: Mike Artin (Massachusetts Institute of Technology), Viktor Ginzburg (University of Chicago), Catharina Stroppel (Universität Bonn , Germany), Toby Stafford* (University of Manchester, United Kingdom), Michel Van den Bergh (Universiteit Hasselt, Belgium), Efim Zelmanov (University of California, San Diego)Over the last few decades noncommutative algebraic geometry (in its many forms) has become increasingly important, both within noncommutative algebra/representation theory, as well as having significant applications to algebraic geometry and other neighbouring areas. The goal of this program is to explore and expand upon these subjects and their interactions. Topics of particular interest include noncommutative projective algebraic geometry, noncommutative resolutions of (commutative or noncommutative) singularities,CalabiYau algebras, deformation theory and Poisson structures, as well as the interplay of these subjects with the algebras appearing in representation theorylike enveloping algebras, symplectic reflection algebras and the many guises of Hecke algebras.
Updated on May 06, 2013 04:21 PM PDT 
Program Complementary Program 201213
Updated on May 21, 2013 12:44 PM PDT 
Program Cluster Algebras
Organizers: Sergey Fomin (University of Michigan), Bernhard Keller (Université Paris Diderot  Paris 7, France), Bernard Leclerc (Université de Caen BasseNormandie, 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 counterintuitive 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, Teichmueller theory, invariant theory, tropical calculus, Poisson geometry, Lie theory, and polyhedral combinatorics.
Updated on May 06, 2013 04:25 PM PDT 
Program Random Spatial Processes
Organizers: Mireille BousquetMélou (Université de Bordeaux I, France), Richard Kenyon* (Brown University), Greg Lawler (University of Chicago), Andrei Okounkov (Columbia 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 twodimensional models of statistical mechanics and random surfaces. Prior to the 1990s the major interests and achievements of probability theory were (with some exceptions for dimensions 4 or more) with respect to onedimensional 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 twodimensional systems and paved the way for a new era of “twodimensional” probability theory.
Updated on Mar 18, 2014 05:04 PM PDT 
Program Quantitative Geometry
Organizers: Keith Ball (University College London, United Kingdom), Emmanuel Breuillard (Université ParisSud 11, France) , Jeff Cheeger (New York University, Courant Institute), Marianna Csornyei (University College London, United Kingdom), Mikhail Gromov (Courant Institute and Institut des Hautes Études Scientifiques, France), Bruce Kleiner (New York University, Courant Institute), Vincent Lafforgue (Université Pierre et Marie Curie, France), 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 nonlinear Banach space theory, quantitative aspects of geometric measure theory and isoperimetry, and metric invariants arising from embedding theory and Riemannian geometry. The MSRI program 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.
Updated on Apr 15, 2014 04:06 PM PDT 
Program Free Boundary Problems, Theory and Applications
Organizers: Luis Caffarelli (University of Texas, Austin), Henri Berestycki (Centre d'Analyse et de Mathématique Sociales, France), Laurence C. Evans (University of California, Berkeley), Mikhail Feldman (University of Wisconsin, Madison), John Ockendon (University of Oxford, United Kingdom), Arshak Petrosyan (Purdue University), Henrik Shahgholian* (The Royal Institute of Technology, Sweden), Tatiana Toro (University of Washington), and Nina Uraltseva (Steklov Mathematical Institute, Russia)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.
Updated on Dec 20, 2013 02:53 PM PST 
Program Arithmetic Statistics
Organizers: Brian Conrey (American Institute of Mathematics), John Cremona (University of Warwick, United Kingdom), Barry Mazur (Harvard University), Michael Rubinstein* (University of Waterloo, Canada ), Peter Sarnak (Princeton University), Nina Snaith (University of Bristol, United Kingdom), 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 Lfunctions has already lead to profound applications regarding among other things the statistics related to arithmetic problems. This program will emphasize statistical aspects of Lfunctions, modular forms, and associated arithmetic and algebraic objects from several different perspectives — theoretical, algorithmic, and experimental.
Updated on Apr 11, 2014 02:24 PM PDT 
Program Random Matrix Theory, Interacting Particle Systems and Integrable Systems
Organizers: 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, France), Craig A. Tracy (University of California, Davis), and Pierre van Moerbeke, (Université Catholique de Louvain, Belgium)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.
Updated on Dec 13, 2013 03:34 PM PST 
Program Inverse Problems and Applications
Organizers: 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, Finland), 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.Updated on Jan 30, 2014 12:50 PM PST 
Program Symplectic and Contact Geometry and Topology
Organizers: Yakov Eliashberg *(Stanford University), John Etnyre (Georgia Institute of Technology), ElenyNicoleta Ionel (Stanford University), Dusa McDuff (Barnard College), and Paul Seidel (Massachusetts Institute of Technology)In the slightly more than two decades that have elapsed since the fields of Symplectic and Contact Topology were created, the field has grown enormously and unforeseen new connections within Mathematics and Physics have been found. The goals of the 200910 program at MSRI are to:
I. Promote the crosspollination of ideas between different areas of symplectic and contact geometry;
II. Help assess and formulate the main outstanding fundamental problems and directions in the field;
III. Lead to new breakthroughs and solutions of some of the main problems in the area;
IV. Discover new applications of symplectic and contact geometry in mathematics and physics;
V. Educate a new generation of young mathematicians, giving them a broader view of the subject and the capability to employ techniques from different areas in their research.
Updated on Apr 14, 2014 09:46 AM PDT 
Program Homology Theories of Knots and Links
Organizers: Mikhail Khovanov (Columbia University), Dusa McDuff (Barnard College), Peter Ozsváth* (Columbia University), Lev Rozansky (University of North Carolina), Peter Teichner (University of California, Berkeley), Dylan Thurston (Barnard College), and Zoltan Szabó (Princeton University)The aims of this program will be to achieve the following goals:
 Promote communication with related disciplines, including the symplectic geometry program in 20092010.
 Lead to new breakthroughs in the subject and find new applications to low dimensional topology (knot theory, threemanifold topology, and smooth four manifold topology).
 Educate a new generation of graduate students and PhD students in this exciting and rapidlychanging subject.
The program will focus on algebraic link homology and Heegaard Floer homology.
Updated on Apr 14, 2014 09:11 AM PDT 
Program Tropical Geometry
Organizers: EvaMaria Feichtner *(University of Bremen), Ilia Itenberg (Institut de Recherche Mathématique Avancée de Strasbourg), Grigory Mikhalkin (Université de Genève), and Bernd Sturmfels (UCB  University of California, Berkeley)Tropical Geometry is the algebraic geometry over the minplus algebra. It is a young subject that in recent years has both established itself as an area of its own right and unveiled its deep connections to numerous branches of pure and applied mathematics. From an algebraic geometric point of view, algebraic varieties over a field with nonarchimedean valuation are replaced by polyhedral complexes, thereby retaining much of the information about the original varieties. From the point of view of complex geometry, the geometric combinatorial structure of tropical varieties is a maximal degeneration of a complex structure on a manifold.
The tropical transition from objects of algebraic geometry to the polyhedral realm is an extension of the classical theory of toric varieties. It opens problems on algebraic varieties to a completely new set of techniques, and has already led to remarkable results in Enumerative Algebraic Geometry, Dynamical Systems and Computational Algebra, among other fields, and to applications in Algebraic Statistics and Statistical Physics.
Updated on Mar 31, 2014 12:47 PM PDT 
Program Algebraic Geometry
Organizers: William Fulton (University of Michigan), Joe Harris (Harvard University), Brendan Hassett (Rice University), János Kollár (Princeton University), Sándor Kovács* (University of Washington), Robert Lazarsfeld (University of Michigan), and Ravi Vakil (Stanford University)Updated on Apr 12, 2014 11:23 AM PDT 
Program Analysis on Singular Spaces
Organizers: Gilles Carron (University of Nantes), Eugenie Hunsicker (Loughborough University), Richard Melrose (Massachusetts Institute of Technology), Michael Taylor (Andras VasyUniversity of North Carolina, Chapel Hill), and Jared Wunsch (Northwestern University)Updated on Apr 04, 2014 04:15 PM PDT 
Program Ergodic Theory and Additive Combinatorics
Organizers: Ben Green (University of Cambridge), Bryna Kra (Northwestern University), Emmanuel Lesigne (University of Tours), Anthony Quas (University of Victoria), Mate Wierdl (University of Memphis)Updated on Apr 01, 2014 02:54 PM PDT 
Program Representation Theory of Finite Groups and Related Topics
Organizers: J. L. Alperin, M. Broue, J. F. Carlson, A. Kleshchev, J. Rickard, B. SrinivasanCurrent research centers on many open questions, i.e., representations over the integers or rings of positive characteristic, correspondence of characters and derived equivalences of blocks. Recently we have seen active interactions in group cohomology involving many areas of topology and algebra. The focus of this program will be on these areas with the goal of fostering emerging interdisciplinary connections among them.
Updated on Apr 15, 2014 02:58 PM PDT 
Program Combinatorial Representation Theory
Organizers: P. Diaconis, A. Kleshchev, B. Leclerc, P. Littelmann, A. Ram, A. Schilling, R. StanleyRecent catalysts stimulating growth of this field in the last few decades have been the discovery of "crystals" and the development of the combinatorics of affine Lie groups.. Today the subject intersects several fields: combinatorics, representation theory, analysis, algebraic geometry, Lie theory, and mathematical physics. The goal of this program is to bring together experts in these areas together in one interdisciplinary setting.
Updated on Apr 15, 2014 05:40 PM PDT 
Program Geometric Group Theory
Organizers: Mladen Bestvina, Jon McCammond, Michah Sageev, Karen VogtmannIn the 1980’s, attention to the geometric structures which cell complexes can carry shed light on earlier combinatorial and topological investigations into group theory, stimulating other provacative and innovative ideas over the past 20 years. As a consequence, geometric group theory has developed many different facets, including geometry, topology, analysis, logic.
Updated on Mar 30, 2014 02:21 PM PDT 
Program Teichmuller Theory and Kleinian Groups
Organizers: Jeffrey Brock, Richard Canary, Howard Masur, Maryam Mirzakhani, Alan ReidThese fields have each seen recent dramatic changes: new techniques developed, major conjectures solved, and new directions and connections forged. Yet progress has been made in parallel without the level of communication across these two fields that is warranted. This program will address the need to strengthen connections between these two fields, and reassess new directions for each.
Updated on Apr 10, 2014 01:42 PM PDT 
Program Geometric Evolution Equations and Related Topics
Organizers: Bennett Chow, Panagiota Daskalopoulos, Gerhardt Huisken, Peter Li, Lei Ni, Gang TianThe focus will be on geometric evolution equations, function theory and related elliptic and parabolic equations. Geometric flows have been applied to a variety of geometric, topological, analytical and physical problems. Linear and nonlinear elliptic and parabolic partial differential equations have been studied by continuous, discrete and computational methods. There are deep connections between the geometry and analysis of Riemannian and Kähler manifolds.
Updated on Apr 03, 2014 10:11 AM PDT 
Program Dynamical Systems
Organizers: Christopher Jones, Jonathan Mattingly, Igor Mezic, Andrew Stuart, LaiSang YoungThis program will take place at the interface of the theory and applications of dynamical systems. The goal will be to assess the current stateoftheart and define directions for future research. Mathematicians who are developing a new generation of ideas in dynamical systems will be brought together with researchers who are using the techniques of dynamical systems in applied areas. A wide range of applications will be considered through four contextual settings around which the program will be organized. Some of the areas of concentration have greater emphasis on extending existing ideas in dynamical systems theory, rendering them more suitable for applications. Others are more directed toward seeking out potential areas of applications in which dynamical systems is likely to have a bigger role to play.
The four themes that will mold the semester are: (1) Extended dynamical systems, (2) Stochastic dynamical systems, (3) Control theory, and (4) Computation and modeling. The introductory workshop, which will be held in midJanuary, will emphasize extended dynamical systems that occur as highdimensional systems, such as on lattices or as partial differential equations. There will be a workshop on stochastic systems and control theory in March. The last theme will pervade the semester through seminar and working group activities.Updated on Apr 10, 2014 03:26 PM PDT 
Program Computational Applications of Algebraic Topology
Organizers: Gunnar Carlsson, Persi Diaconis, Susan Holmes, Rick Jardine, Günter M. ZieglerUpdated on Apr 08, 2014 01:37 PM PDT 
Program New Topological Structures in Physics
Organizers: M. Aganagic, R. Cohen, P. Horava, A. Klemm, J. Morava, H. Nakajima, Y. RuanThe interplay between quantum field theory and mathematics during the past several decades has led to new concepts of mathematics, which will be explored and developed in this program. This includes: Stringy topology, branes and orbifolds, Generalized McKay correspondences and representation theory and GromovWitten theory.
Updated on Apr 15, 2014 01:29 PM PDT 
Program Rational and Integral Points on HigherDimensional Varieties
Organizers: Fedor Bogomolov, JeanLouis ColliotThélène, Bjorn Poonen, Alice Silverberg, Yuri TschinkelOur focus will be rational and integral points on varieties of dimension > 1. Recently it has become clear that many branches of mathematics can be brought to bear on problems in the area: complex algebraic geometry, Galois and 4etale cohomology, transcendence theory and diophantine approximation, harmonic analysis, automorphic forms, and analytic number theory. Sometimes it is only by combining techniques that progress is made. We will bring together researchers from these various fields who have an interest in arithmetic applications, as well as specialists in arithmetic geometry itself.
Updated on Apr 16, 2014 05:30 AM PDT 
Program Nonlinear Dispersive Equations
Organizers: Carlos Kenig, Sergiu Klainerman, Christophe Sogge, Gigliola Staffilani, Daniel TataruThe field of nonlinear dispersive equations has experienced a striking evolution over the last fifteen years. During that time many new ideas and techniques emerged, enabling one to work on problems which until quite recently seemed untouchable. The evolution process for this field has itsorigin in two ways of quantitatively measuring dispersion. One comes from harmonic analysis, which is used to establish certain dispersive (Lp) estimates for solutions to linear equations. The second has geometrical roots, namely in the analysis of vector fields generating the Lorentz groupassociated to the linear wave equation. Our semester program in nonlinear dispersive equations will bring together leading experts in both of these directions.
Updated on Mar 20, 2014 06:13 PM PDT 
Program Nonlinear Elliptic Equations and Its Applications
Organizers: Xavier Cabré, Luis Caffarelli, Lawrence C. Evans, Cristian Gutiérrez, Lihe Wang, Paul YangThe research in nonlinear elliptic equations is one of the most developed in Mathematics, and of great importance because of its interaction with other areas within Mathematics and for its applications in broader scientific disciplines such as fluid dynamics, phase transitions, mathematical finance and image processing in computer science.
Updated on Feb 18, 2014 11:13 AM PST 
Program Computing the Continuous Discretely: Integer Point Enumeration in Polyhedra (Summer Graduate Program)
Organizers: Mathias Beck and Sinai RobinsUpdated on Feb 18, 2014 03:21 PM PST 
Program CR Geometry: Complex Analysis Meets Real Geometry and Number Theory
Organizers: John D’AngeloUpdated on Apr 09, 2014 06:16 AM PDT 
Program Clay Mathematics Institute 2005 Summer School Ricci Flow, 3 Manifolds And Geometry
Organizers: Gang Tian, John Lott, John Morgan, Bennett Chow, Tobias Colding, Jim Carlson, David Ellwood, Hugo RossiGraduate Students from MSRI Sponsoring Institutions may benominated to participate in this program.
Updated on Apr 09, 2014 06:16 AM PDT 
Program Mathematical Graphics (Summer Graduate Program)
Organizers: David Austin, Bill Casselman and Jim FixUpdated on Sep 06, 2013 10:32 AM PDT 
Program AMSIMSSIAM Summer School in Commutative Algebra: Local Cohomology and Its Applications
Organizers: Anurag Singh and Uli WaltherGraduate Students from MSRI Sponsoring Institutions may benominated to participate in this program.
Updated on Dec 19, 2013 01:14 PM PST 
Program Graduate Student WarmUp Workshop in Algebraic Geometry
Organizers: Sándor Kovács, Tony Pantev, and Ravi VakilGraduate Students from MSRI Sponsoring Institutions may benominated to participate in this program.
Updated on Apr 06, 2014 11:32 PM PDT 
Program Probability, Algorithms and Statistical Physics
Organizers: Yuval Peres (cochair), Alistair Sinclair (cochair), David Aldous, Claire Kenyon, Harry Kesten, Jon Kleinberg, Fabio Martinelli, Alan Sokal, Peter Winkler, Uri ZwickUpdated on Mar 05, 2014 09:31 AM PST 
Program Mathematical, Computational and Statistical Aspects of Image Analysis
Organizers: David Mumford (Brown University), Jitendra Malik (University of California, Berkeley), Donald Geman (John Hopkins University) and David Donoho (Stanford University)The field of image analysis is one of the newest and most active sources of inspiration for applied mathematics. Present day mathematical challenges in image analysis span a wide range of mathematical territory.
Updated on Mar 14, 2014 10:46 AM PDT 
Program Hyperplane Arrangements and Application
Organizers: Michael Falk, Phil Hanlon, Toshitake Kohno, Peter Orlik, Alexander Varchenko, Sergey YuzvinskyThe theory of complex hyperplane arrangements has undergone tremendous growth since its beginnings thirty years ago in the work of Arnol'd, Breiskorn, Deligne, and Hattori. Connections with generalized hypergeometric functions, conformal field theory, representations of braid groups, and other areas have stimulated fascinating research into topology of arrangement complements. Topological research leads in turn to many new combinatorial and algebraic questions about arrangements.
Updated on Apr 15, 2014 05:40 PM PDT 
Program Summer Graduate Program in Hyperplane Arrangements and Applications (Summer Graduate Program)
Organizers: Sergey YuzvinskyThis MSRI Summer Graduate Program at the University of Oregon will provide an introduction to the material to be covered in the fall, 2004 MSRI program on Hyperplane Arrangements and Applications. See the program page for more information on the content.
Created on May 29, 2005 02:19 AM PDT 
Program SGP: Knot Theory and 3Manifolds
Organizers: Steven Boyer, Roger A Fenn and Dale RolfsenOpen only to graduate students nominated by MSRI's Academic Sponsors.
Updated on Jan 15, 2014 12:34 PM PST 
Program SGP: Analysis of Algorithms
Organizers: P. Flajolet, G. Seroussi, W. Szpankowski, and M. WeinbergerPlease note, MSRI's Summer Graduate Programs are open only to students nominated by MSRI's Academic Sponsor universities.
Updated on Feb 19, 2014 09:09 AM PST 
Program Differential Geometry
Organizers: Robert Bryant (cochair), Frances Kirwan, Peter Petersen, Richard Schoen, Isadore Singer, and Gang Tian (cochair)As classical as the subject is, it is currently undergoing a very vigorous development, interacting strongly with theoretical physics, mechanics, topology, algebraic geometry, partial differential equations, the calculus of variations, integrable systems, and many other subjects. The five main topics on which we propose to concentrate the program are areas that have shown considerable growth in the last ten years: Complex geometry, calibrated geometries and special holonomy; Geometric analysis; Symplectic geometry and gauge theory; Geometry and physics; Riemannian and metric geometry.
Updated on Apr 03, 2014 10:56 AM PDT 
Program Topological Aspects of Real Algebraic Geometry
Organizers: Selman Akbulut, Grisha Mikhalkin, Victoria Powers, Boris Shapiro, Frank Sottile (chair), and Oleg ViroThe topological approach to real algebraic geometry is due to Hilbert who realized the advantages of considering topological properties of real algebraic plane curves. Much progress on Hilbert's work was achieved in the 1970's by the schools of Rokhlin and Arnold, including new objects and questions on complexification and complex algebraic geometry, relation to piecewise linear geometry and combinatorics, and enumerative geometry. This continues today with new topics such as amoebas, new connections such as that with symplectic geometry, and new challenges such as those posed by real polynomial systems.
Updated on Mar 31, 2014 12:47 PM PDT 
Program Discrete and Computational Geometry
Organizers: Jesús A. De Loera, Herbert Edelsbrunner, Jacob E. Goodman, János Pach, Micha Sharir, Emo Welzl, and Günter M. ZieglerDiscrete and Computational Geometry deals with the structure and complexity of discrete geometric objects as well with the design of efficient computer algorithms for their manipulation. This area is by its nature interdisciplinary and has relations to many other vital mathematical fields, such as algebraic geometry, topology, combinatorics, and probability theory; at the same time it is on the cutting edge of modern applications such as geographic information systems, mathematical programming, coding theory, solid modeling, and computational structural biology.
Updated on Apr 10, 2014 05:36 PM PDT 
Program SGP: Triangulations of Point Sets: Applications, Structures, Algorithms
Organizers: Jesús A. De Loera, Jörg Rambau, and Francisco SantosPlease note, MSRI's Summer Graduate Programs are open only to students nominated by MSRI's Academic Sponsor universities.
Updated on Apr 08, 2014 01:37 PM PDT 
Program SGP: Mathematical Graphics
Organizers: Bill Casselman and David AustinPlease note, MSRI's Summer Graduate Programs are open only to students nominated by MSRI's Academic Sponsor universities.
Updated on Feb 19, 2014 08:57 AM PST 
Program Commutative Algebra
Organizers: Luchezar Avramov, Mark Green, Craig Huneke, Karen E. Smith and Bernd SturmfelsCommutative algebra comes from several sources, the 19th century theory of equations, number theory, invariant theory and algebraic geometry. The field has experienced a striking evolution over the last fifteen years. During that period the outlook of the subject has been altered, new connections to other areas have been established, and powerful techniques have been developed.
Updated on Apr 14, 2014 10:21 PM PDT 
Program SemiClassical Analysis
Organizers: Robert Littlejohn, William H. Miller, Johannes Sjorstrand, Steven Zelditch, and Maciej ZworskiThe traditional mathematical study of semiclassical analysis has developed tremendously in the last thirty years following the introduction of microlocal analysis, that is local analysis in phase space, simultaneously in the space and Fourier transform variables. The purpose of this program is to bring together experts in traditional mathematical semiclassical analysis, in the new mathematics of "quantum chaos," and in physics and theoretical chemistry.
Updated on Apr 03, 2014 10:56 AM PDT 
Program Quantum Computation
Organizers: Dorit Aharonov, Charles Bennett, Richard Jozsa, Yuri Manin, Peter Shor, and Umesh Vazirani (chair)Quantum computation is an intellectually challenging and exciting area that touches on the foundations of both computer science and quantum physics.
Updated on Mar 20, 2014 08:42 PM PDT 
Program SGP: Biomathematics, Bioengineering & Clinical Aspects of Blood Flow
Organizers: Stanley A. Berger, Giovanni P. Galdi (cochair), Charles S. Peskin, Alfio Quarteroni, Anne M. Robertson (cochair), Adélia Sequeira, and Howard YonasSummer Graduate Program  open only to students nominated by MSRI's Academic Sponsor universities.
Updated on Jan 14, 2014 06:38 PM PST 
Program SGP: Excursions in Computational Number Theory  Polynomials with Integer Coefficients
Organizers: Peter Borwein and Michael FilasetaSummer Graduate Program  open only to students nominated by MSRI's Academic Sponsor universities, to be held in Vancouver, BC, Canada at the Pacific Institute of Mathematics facility of Simon Fraser University.
Updated on Jan 06, 2014 11:11 AM PST 
Program InfiniteDimensional Algebras and Mathematical Physics
Organizers: E. Frenkel, V. Kac, I. Penkov, V. Serganova, G. ZuckermanThis program will discuss recent progress in the representation theory of infinitedimensional algebras and superalgebras and their applications to other fields.
Updated on Apr 10, 2014 10:53 AM PDT 
Program Algebraic Stacks, Intersection Theory, and NonAbelian Hodge Theory
Organizers: W. Fulton, L. Katzarkov, M. Kontsevich, Y. Manin,R. Pandharipande, T. Pantev, C. Simpson and A. VistoliAlgebraic stacks originally arose as solutions to moduli problems in which they were used to parametrize geometric objects in families.They have also arisen in studying homological properties of quotient singularities, nonabelian Hodge theory, string theory, etc. This program will focus on intersection theory on stacks, nonabelian Hodge theory and geometric nstacks, perverse sheaves on stacks and the geometric Langlands program, Dbrane charges in string theory, and moduli of gerbes and mirror symmetry.
Updated on Mar 25, 2014 08:40 PM PDT 
Program Integral Geometry
Organizers: L. Barchini, S. Gindikin, A. Goncharov and J. WolfThis program will focus on recent advances in integral geometry,with a focus on theinterrelationships between integral geometry and the theory ofrepresentations (Penrosetransform in flag domains, horospherical transforms), complex geometry, symplectic geometry,algebraic analysis, and nonlinear differential equations.
There will be an Introductory Workshop in Inverse Problems and Integral Geometry August 1324Updated on Mar 13, 2014 07:52 PM PDT 
Program Inverse Problems
Organizers: D. Colton, J. McLaughlin, W. Symes and G. UhlmannIn the last twenty years or so there have been substantial developments in the mathematical theory of inverse problems,and applications have arisen in many areas, ranging from geophysics to medical imaging to nondestructive evaluation of materials. The main topics of this program will be developments in inverse boundary value problems, and inverse scattering problems.
There will be an Introductory Workshop in Inverse Problems and Integral Geometry August 1324Updated on Jan 30, 2014 12:50 PM PST 
Program SGP: The Global Theory of Minimal Surfaces
Organizers: Joel Hass and David HoffmanMSRI's second Graduate Summer Program for 2001.
Updated on Apr 08, 2014 07:25 PM PDT 
Program SGP: Modern Signal Processing
Organizers: Dan Rockmore and Dennis HealyMSRI's Summer Graduate Program I This summer graduate program, organized by Dan Rockmore and Dennis Healy, Jr., will introduce students to the world of signal processing. The course will cover standard tools of digital signal processing, but will also cover the exciting frontiers of the subject, including wavelets, ISP (integrated sensing and processing), image processing algorithms, etc. In addition, students will be briefly exposed to applications in various areas, such as biology, chemistry, medicine, music, and engineering.
Updated on Jan 14, 2014 06:38 PM PST 
Program Operator Algebras
Organizers: C. AnantharamanDelaroche, H. Araki, A. Connes, J. Cuntz, E.G. Effros, U. Haagerup, V.F.R. Jones , M.A. Rieffel and D.V. VoiculescuThe noncommutative mathematics of operator algebras has grown in many directions and has made unexpected connections with other parts of mathematics and physics. Since the 198485 MSRI program in Operator Algebras, developments have continued at a rapid pace, and interactions with other fields such as elementary particle physics and quantum groups continue to grow.
Updated on Apr 02, 2014 12:35 PM PDT 
Program Spectral Invariants
Organizers: Tom Branson, S.Y. Alice Chang, Rafe Mazzeo and Kate OkikioluThe past few decades have witnessed many new developments in the broad area of spectral theory of geometric operators, centered around the study of new spectral invariants and their application to problems in conformal geometry, classification of 4manifolds, index theory, relationship with scattering theory and other topics. This program will bring together people working on different problems in these areas.
Updated on Apr 03, 2014 10:56 AM PDT 
Program Algorithmic Number Theory
Organizers: Joe Buhler, Cynthia Dwork, Hendrik Lenstra Jr., Andrew Odlyzko, Bjorn Poonen and Noriko YuiNumber theorists have always made calculations, whether by hand, desk calculator, or computer. In recent years this predilection has extended in many directions, and has been reinforced by interest from other fields such as computer science, cryptography, and algebraic geometry. The Algorithmic Number Theory program at MSRI will cover these developments broadly, with an eye to making connections to some of these other areas.
Updated on Apr 15, 2014 09:21 AM PDT 
Program SGP: Combinatorial Game Theory
Organizers: E. Berlekamp, D. WolfeSUMMER GRADUATE PROGRAMFor more information about this program, please see the original web page at:http://www.msri.org/calendar/sgp/sgp2/index.html
Updated on Apr 03, 2014 10:56 AM PDT 
Program Noncommutative Algebra
Organizers: Michael Artin, Susan Montgomery, Claudio Procesi, Lance Small, Toby Stafford, Efim ZelmanovFor more information about this program, please see the original web page at:http://www.msri.org/activities/programs/9900/noncomm/index.html
Updated on Mar 31, 2014 06:23 PM PDT 
Program SGP: Mathematical and Computational Challenges In Molecular and Cell Biology
Organizers: Nicholas R. Cozzarelli, Michael Levitt, Wilma Olson, De Witt SumnersSUMMER GRADUATE PROGRAMFor more information about this program, please see the original web page at:http://www.msri.org/calendar/workshops/9900/Molecular_and_Cell_Biology/index.html
Updated on Feb 19, 2014 08:58 AM PST 
Program Numerical and Applied Mathematics
Organizers: Ivo Babuska, M. Vogelius, L. Wahlbin, R. Bank and D. ArnoldFor more information about this program, please see the original web page at:http://www.msri.org/activities/programs/9900/fem/index.html
Updated on Feb 19, 2014 08:58 AM PST 
Program Galois Groups and Fundamental Groups
Organizers: Eva Bayer, Michael Fried, David Harbater, Yasutaka Ihara, B. Heinrich Matzat, Michel Raynaud, John ThompsonFor more information about this event, please see the original web page at:http://www.msri.org/activities/programs/9900/galois/index.html
Updated on Apr 14, 2014 12:52 PM PDT 
Program SGP: Lie groups and the method of the moving frame / Exterior Differential Systems
Organizers: Jeanne N. Clelland and Robert Bryant,For more information, please see this programs original web page at http://www.msri.org/activities/events/9899/sgp99/bryant.html
Updated on Feb 04, 2014 08:40 PM PST 
Program SGP: Nonlinear dynamics of lowdimensional continua
Organizers: L. Mahadevan and Anette HosoiFor more information, please see the original program page at http://www.msri.org/activities/events/9899/sgp99/mahadevan.html
Updated on Oct 14, 2013 03:55 PM PDT 
Program Random Matrix Models and Their Applications
Organizers: Pavel Bleher (coChair), Alan Edelman, Alexander Its (coChair), Craig Tracy and Harold WidomFor more information about this program, please see the program's original web page at http://www.msri.org/activities/programs/9899/random/index.html
Updated on Apr 03, 2014 10:56 AM PDT 
Program Foundations of Computational Mathematics
Organizers: Felipe Cucker (coChair), Arieh Iserles (coChair), Tien Yien Li, Mike Overton, Jim Renegar, Mike Shub (coChair), Steve Smale, and Andrew StuartPlease see the program's webpage at http://www.msri.org/activities/programs/9899/focm/index.html for more information.
Updated on Apr 10, 2014 03:26 PM PDT 
Program Symbolic Computation in Geometry and Analysis
Organizers: MarieFrancoise Roy, Michael Singer (Chair) and Bernd SturmfelsPlease see the program webpage at http://www.msri.org/activities/programs/9899/symbcomp/index.html for more information.
Updated on Apr 15, 2014 06:19 AM PDT 
Program SGP: Algorithmic Algebra and Geometry
Organizers: David Bayer, Sorin PopescuUpdated on Mar 26, 2014 11:28 AM PDT 
Program Stochastic Analysis
Organizers: R. Banuelos, S. Evans, P. Fitzsimmons, E. Pardoux, D. Stroock, and R. WilliamsPlease see the program webpage at http://www.msri.org/activities/programs/9798/sa/index.html for more information.
Updated on Apr 14, 2014 04:24 PM PDT 
Program Model Theory of Fields
Organizers: Elisabeth Bouscaren, Lou van den Dries, Ehud Hrushovski, David Marker (coChair), Anand Pillay, Jose Felipe Voloch, and Carol Wood (coChair)Please see the program webpage at http://www.msri.org/activities/programs/9798/mtf/index.html for more information about this program.
Updated on Apr 15, 2014 11:55 AM PDT 
Program Harmonic Analysis
Organizers: Michael Christ, David Jerison, Carlos Kenig (Chair), Jill Pipher, and Elias Stein.Please see the program webpage at http://www.msri.org/activities/programs/9798/ha/index.html for more information.
Updated on Mar 20, 2014 06:13 PM PDT 
Program Lowdimensional Topology
Organizers: Joan Birman, Andrew Casson, Robion Kirby (Chair), and Ron SternPlease see the program webpage at http://www.msri.org/activities/programs/9697/ldt/index.html for more information.
Updated on Apr 14, 2014 09:11 AM PDT 
Program SGP: Cryptography
Organizers: Neal Koblitz, Alfred MenezesUpdated on Feb 19, 2014 09:07 AM PST 
Program Combinatorics
Organizers: Louis Billera, Anders Bjorner, Curtis Greene, Rodica Simion, and Richard Stanley (Chair)Please see the program webpage at http://www.msri.org/activities/programs/9697/comb/index.html for more information.
Updated on Apr 15, 2014 05:40 PM PDT 
Program Several Complex Variables
Organizers: JeanPierre Demailly, Joseph J. Kohn, Junjiro Noguchi, Linda Rothschild, Michael Schneider, and YumTong Siu (Chair)Please see the program webpage at http://www.msri.org/activities/programs/9596/scv/ for more information.
Updated on Jan 09, 2014 08:57 AM PST 
Program Convex Geometry and Geometric Functional Analysis
Organizers: Keith Ball, Eric Carlen, Erwin Lutwak, V. D. Milman, E. Odell, and N. Tomczak.Updated on Dec 08, 2013 06:21 PM PST 
Program SGP: Algebra, Algorithms, and Approximation
Organizers: Dave Bayer, Ilan Vardi, John StrainUpdated on Mar 27, 2014 11:05 AM PDT 
Program Holomorphic Spaces
Organizers: Sheldon Axler (coChair), John McCarthy (coChair), Don Sarason (coChair), Joseph Ball, Nikolai Nikolskii, Mihai Putinar, and Cora SadoskyPlease see the program webpage at http://www.msri.org/activities/programs/9596/hs/ for more information.
Updated on Oct 18, 2013 01:38 PM PDT 
Program SGP: Random Walk and Geometry
Organizers: Persi Diaconis, Laurent SaloffCosteUpdated on Apr 08, 2014 07:25 PM PDT 
Program Complex Dynamics and Hyperbolic Geometry
Organizers: Bodil Branner, Steve Kerckhoff, Mikhail Lyubich, Curt McMullen (chair), and John SmillieUpdated on Mar 30, 2014 10:07 AM PDT 
Program Automorphic Forms
Organizers: Daniel Bump, Stephen Gelbart, Dennis Hejhal, Jeff Hoffstein (cochairman), Steve Rallis (cochairman), and Marie France VignerasUpdated on Apr 08, 2014 08:34 AM PDT 
Program SGP: Hyperbolic Geometry
Organizers: William P. Thurston, Jane Gilman, David EpsteinUpdated on Apr 09, 2014 06:16 AM PDT 
Program Dynamical Systems and Probabilistic Methods for PDE's
Organizers: Percy Deift (cochairman), Philip Holmes, James Hyman, David Levermore, David McLaughlin (cochairman), Clarence Eugene WayneUpdated on Mar 14, 2014 11:26 AM PDT 
Program Differential Geometry
Organizers: Werner Ballman, Raoul Bott, Carolyn Gordon, Mikhael Gromov, Karsten Grove, Blaine Lawson (chairman), Richard SchoenUpdated on Apr 14, 2014 11:09 AM PDT 
Program SGP: Automorphic Forms and Zeta Functions
Organizers: Dan Bump, Dinakar RamakrishnanUpdated on Mar 27, 2014 10:59 AM PDT 
Program Transcendence and Diophantine Problems
Organizers: A. Baker (cochairman), W. Brownawell, W. Schmidt (co chairman), P. VojtaUpdated on Apr 15, 2014 06:19 AM PDT 
Program Algebraic Geometry
Organizers: E. Arbarello, A. Beauville, A. Beilinson, J. Harris, W. Fulton, J. Kollar, S. Mori, J. Steenbrink, H. Clemens & J. KollarUpdated on Apr 12, 2014 11:23 AM PDT 
Program Symbolic Dynamics
Organizers: R. Adler (chairman), J. Franks, D. Lind, S. WilliamsUpdated on Feb 14, 2014 04:29 AM PST 
Program SGP: Mathematical Biology
Organizers: N. Kopell, C. Peskin, M. Reed (chairman), J. RinzelCreated on May 29, 2005 02:19 AM PDT 
Program Lie Groups and Ergodic Theory with Applications to Number Theory and Geometry
Organizers: H. Furstenberg, M. Ratner, P. Sarnak, R. Zimmer (chairman)Updated on Apr 15, 2014 07:57 AM PDT 
Program Statistics
Organizers: P. Bickel (chairman), L. LeCam, D. Siegmund, T. SpeedUpdated on Mar 14, 2014 10:46 AM PDT 
Program Strings in Mathematics and Physics
Organizers: O. Alvarez, D. Friedan, G. Moore, I.M. Singer (chairman), G. Segal, C. TaubesUpdated on Apr 14, 2014 11:09 AM PDT 
Program Partial Differential Equations and Continuum Mechanics
Organizers: L.C. Evans, A. Majda (chairman), G. Papanicolaou, T. SpencerUpdated on Mar 14, 2014 11:26 AM PDT 
Program SGP: 4Manifolds
Organizers: Rob Kirby, Ron SternUpdated on Mar 05, 2014 09:47 AM PST 
Program Representations of Finite Groups
Organizers: J. Alperin, C. Curtis (chairman), W. Feit, P. FongUpdated on Oct 01, 2013 11:08 AM PDT 
Program Logic
Organizers: L. Harrington, A. Macintyre, D.A. Martin (chairman), R. ShoreUpdated on Apr 15, 2014 11:54 AM PDT 
Program Algebraic Topology and its Applications
Organizers: R. Cohen (chairman), G. Carlsson, W.C. Hsiang, J.D.S. JonesUpdated on Apr 15, 2014 02:55 PM PDT 
Program Combinatorial Group Theory and Geometry
Organizers: S. Adian, K. Brown, S. Gersten, J. Stallings (chairman)Updated on Feb 18, 2014 12:46 AM PST 
Program Symplectic Geometry and Mechanics
Organizers: R. Devaney, V. Guillemin (cochairman), H. Flaschka, A. Weinstein (cochairman)Updated on Mar 31, 2014 03:41 PM PDT 
Program Classical Analysis
Organizers: C. Fefferman, E. Stein (chairman), G. WeissUpdated on Mar 18, 2014 04:47 PM PDT 
Program Representations of Lie Groups
Organizers: W. Schmid, D. Vogan, J. Wolf (chairman)Updated on Apr 08, 2014 08:34 AM PDT 
Program Number Theory with Connections to Algebraic Geometry
Organizers: B. Gross (chairman), N. Katz, B. Mazur, K. Ribet, J. TateUpdated on Apr 15, 2014 11:44 AM PDT 
Program Geometric Function Theory
Organizers: D. Drasin, F. Gehring (chairman), I. Kra, A. MardenUpdated on Apr 10, 2014 01:42 PM PDT 
Program Mathematical Economics
Organizers: K. Arrow, G. Debreu (chairman), A. MasColellUpdated on Mar 18, 2014 05:06 PM PDT 
Program Computational Complexity
Organizers: R. Graham, R. Karp (cochairman), S. Smale (cochairman)Updated on Mar 10, 2014 04:37 PM PDT 
Program Differential Geometry
Organizers: S.S. Chern (chairman), B. Lawson, I. M. Singer (miniprogram)Updated on Sep 18, 2013 02:59 PM PDT 
Program Lowdimensional Topology
Organizers: R. Edwards (chairman), R. Kirby, J. Morgan, W. ThurstonUpdated on Mar 25, 2014 08:40 PM PDT 
Program KTheory, Index Theory, and Operator Algebras
Organizers: A. Connes (chairman), R. Douglas, M. TakesakiUpdated on Apr 15, 2014 03:11 PM PDT 
Program InfiniteDimensional Lie Algebras
Organizers: H. Garland, I. Kaplansky (chairman), B. KostantUpdated on Sep 09, 2013 03:25 PM PDT 
Program Ergodic Theory and Dynamical Systems
Organizers: J. Feldman (chairman), J. Franks, A. Katok, J. Moser, R. TemamUpdated on Feb 17, 2014 01:39 PM PST 
Program Mathematical Statistics
Organizers: L. LeCam, D. Siegmund (chairman), C. StoneUpdated on Sep 13, 2013 09:40 AM PDT 
Program Nonlinear Partial Differential Equations
Organizers: A. Chorin, I. M. Singer (chairman), S.T. YauUpdated on Apr 03, 2014 10:56 AM PDT

Past Programs
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