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Past Programs

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  1. Program Model Theory, Arithmetic Geometry and Number Theory

    Organizers: Ehud Hrushovski (Hebrew University), François Loeser (Université de Paris VI (Pierre et Marie Curie)), David Marker (University of Illinois), Thomas Scanlon (University of California, Berkeley), Sergei Starchenko (University of Notre Dame), LEAD Carol Wood (Wesleyan University)

    The program aims to further the flourishing interaction between model theory and other parts of mathematics, especially number theory and arithmetic geometry. At present the model theoretical tools in use arise primarily from geometric stability theory and o-minimality. Current areas of lively interaction include motivic integration, valued fields, diophantine geometry, and algebraic dynamics.

    Updated on Feb 19, 2014 02:02 PM PST
  2. Program Algebraic Topology

    Organizers: Vigleik Angeltveit (Australian National University), Andrew Blumberg (University of Texas), Gunnar Carlsson (Stanford University), Teena Gerhardt (Michigan State University), LEAD Michael Hill (University of Virginia), Jacob Lurie (Harvard University)

    Algebraic topology touches almost every branch of modern mathematics. Algebra, geometry, topology, analysis, algebraic geometry, and number theory all influence and in turn are influenced by the methods of algebraic topology. The goals of this 2014 program at MSRI are:

    Bring together algebraic topology researchers from all subdisciplines, reconnecting the pieces of the field

    Identify the fundamental problems and goals in the field, uncovering the broader themes and connections

    Connect young researchers with the field, broadening their perspective and introducing them to the myriad approaches and techniques.

    Updated on Jan 21, 2014 11:44 AM PST
  3. Program Mathematical General Relativity

    Organizers: Yvonne Choquet-Bruhat, Piotr Chrusciel (Universität Wien), Greg Galloway (University of Miami), Gerhard Huisken (Math. 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 semester-long 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
  4. 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 (Max-Planck-Institut 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 long-standing 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
  5. 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 year-long 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
  6. 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,Calabi-Yau algebras, deformation theory and Poisson structures, as well as the interplay of these subjects with the algebras appearing in representation theory--like enveloping algebras, symplectic reflection algebras and the many guises of Hecke algebras.

    Updated on May 06, 2013 04:21 PM PDT
  7. Program Cluster Algebras

    Organizers: Sergey Fomin (University of Michigan), Bernhard Keller (Université Paris Diderot - Paris 7, France), Bernard Leclerc (Université de Caen Basse-Normandie, 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, Teichmueller theory, invariant theory, tropical calculus, Poisson geometry, Lie theory, and polyhedral combinatorics.

    Updated on May 06, 2013 04:25 PM PDT
  8. Program Random Spatial Processes

    Organizers: Mireille Bousquet-Mélou (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 two-dimensional 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 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.

    Updated on Oct 18, 2014 12:24 PM PDT
  9. Program Quantitative Geometry

    Organizers: Keith Ball (University College London, United Kingdom), Emmanuel Breuillard (Université Paris-Sud 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 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 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 Oct 22, 2014 11:15 AM PDT
  10. 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 Aug 28, 2014 12:01 PM PDT
  11. 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 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.

    Updated on Oct 21, 2014 12:32 PM PDT
  12. 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 Aug 14, 2014 02:44 PM PDT
  13. 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 Sep 09, 2014 01:03 PM PDT
  14. Program Symplectic and Contact Geometry and Topology

    Organizers: Yakov Eliashberg *(Stanford University), John Etnyre (Georgia Institute of Technology), Eleny-Nicoleta 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 2009-10 program at MSRI are to:
    I. Promote the cross-pollination 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 19, 2014 09:30 PM PDT
  15. 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:

    1. Promote communication with related disciplines, including the symplectic geometry program in 2009-2010.
    2. Lead to new breakthroughs in the subject and find new applications to low dimensional topology (knot theory, three-manifold topology, and smooth four manifold topology).
    3. Educate a new generation of graduate students and PhD students in this exciting and rapidly-changing subject.

    The program will focus on algebraic link homology and Heegaard Floer homology.

    Updated on Sep 30, 2014 07:36 PM PDT
  16. Program Tropical Geometry

    Organizers: Eva-Maria 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 min-plus 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 non-archimedean 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 Sep 11, 2014 11:23 AM PDT
  17. 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 Oct 22, 2014 11:39 AM PDT
  18. 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 Sep 15, 2014 06:10 PM PDT
  19. 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 Oct 13, 2014 04:42 PM PDT
  20. Program Representation Theory of Finite Groups and Related Topics

    Organizers: J. L. Alperin, M. Broue, J. F. Carlson, A. Kleshchev, J. Rickard, B. Srinivasan

    Current 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 Oct 22, 2014 09:53 AM PDT
  21. Program Combinatorial Representation Theory

    Organizers: P. Diaconis, A. Kleshchev, B. Leclerc, P. Littelmann, A. Ram, A. Schilling, R. Stanley

    Recent 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 Oct 22, 2014 06:23 PM PDT
  22. Program Geometric Group Theory

    Organizers: Mladen Bestvina, Jon McCammond, Michah Sageev, Karen Vogtmann

    In 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 Oct 02, 2014 05:14 PM PDT
  23. Program Teichmuller Theory and Kleinian Groups

    Organizers: Jeffrey Brock, Richard Canary, Howard Masur, Maryam Mirzakhani, Alan Reid

    These 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 Oct 22, 2014 07:40 AM PDT
  24. Program Geometric Evolution Equations and Related Topics

    Organizers: Bennett Chow, Panagiota Daskalopoulos, Gerhardt Huisken, Peter Li, Lei Ni, Gang Tian

    The 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 Oct 19, 2014 06:10 AM PDT
  25. Program Dynamical Systems

    Organizers: Christopher Jones, Jonathan Mattingly, Igor Mezic, Andrew Stuart, Lai-Sang Young

    This program will take place at the interface of the theory and applications of dynamical systems. The goal will be to assess the current state-of-the-art 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 mid-January, will emphasize extended dynamical systems that occur as high-dimensional 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 Jul 03, 2014 04:41 PM PDT
  26. Program New Topological Structures in Physics

    Organizers: M. Aganagic, R. Cohen, P. Horava, A. Klemm, J. Morava, H. Nakajima, Y. Ruan

    The 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 Gromov-Witten theory.

    Updated on Oct 18, 2014 12:24 PM PDT
  27. Program Rational and Integral Points on Higher-Dimensional Varieties

    Organizers: Fedor Bogomolov, Jean-Louis Colliot-Thélène, Bjorn Poonen, Alice Silverberg, Yuri Tschinkel

    Our 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 Oct 21, 2014 02:39 PM PDT
  28. Program Nonlinear Dispersive Equations

    Organizers: Carlos Kenig, Sergiu Klainerman, Christophe Sogge, Gigliola Staffilani, Daniel Tataru

    The 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 Jul 28, 2014 08:22 PM PDT
  29. Program Nonlinear Elliptic Equations and Its Applications

    Organizers: Xavier Cabré, Luis Caffarelli, Lawrence C. Evans, Cristian Gutiérrez, Lihe Wang, Paul Yang

    The 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 Oct 03, 2014 12:27 PM PDT
  30. Program Graduate Student Warm-Up Workshop in Algebraic Geometry

    Organizers: Sándor Kovács, Tony Pantev, and Ravi Vakil

    Graduate Students from MSRI Sponsoring Institutions may benominated to participate in this program.

    Updated on Sep 04, 2014 03:15 PM PDT
  31. Program Probability, Algorithms and Statistical Physics

    Organizers: Yuval Peres (co-chair), Alistair Sinclair (co-chair), David Aldous, Claire Kenyon, Harry Kesten, Jon Kleinberg, Fabio Martinelli, Alan Sokal, Peter Winkler, Uri Zwick

    Updated on Sep 04, 2014 02:12 PM PDT
  32. 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 Oct 21, 2014 11:15 AM PDT
  33. Program Hyperplane Arrangements and Application

    Organizers: Michael Falk, Phil Hanlon, Toshitake Kohno, Peter Orlik, Alexander Varchenko, Sergey Yuzvinsky

    The 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 Oct 22, 2014 06:23 PM PDT
  34. Program SGP: Knot Theory and 3-Manifolds

    Organizers: Steven Boyer, Roger A Fenn and Dale Rolfsen

    Open only to graduate students nominated by MSRI's Academic Sponsors.

    Updated on Sep 11, 2014 09:57 AM PDT
  35. Program SGP: Analysis of Algorithms

    Organizers: P. Flajolet, G. Seroussi, W. Szpankowski, and M. Weinberger

    Please note, MSRI's Summer Graduate Programs are open only to students nominated by MSRI's Academic Sponsor universities.

    Updated on Sep 05, 2014 04:30 PM PDT
  36. Program Differential Geometry

    Organizers: Robert Bryant (co-chair), Frances Kirwan, Peter Petersen, Richard Schoen, Isadore Singer, and Gang Tian (co-chair)

    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 Sep 28, 2014 11:56 AM PDT
  37. Program Topological Aspects of Real Algebraic Geometry

    Organizers: Selman Akbulut, Grisha Mikhalkin, Victoria Powers, Boris Shapiro, Frank Sottile (chair), and Oleg Viro

    The 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 Oct 18, 2014 12:24 PM PDT
  38. Program Discrete and Computational Geometry

    Organizers: Jesús A. De Loera, Herbert Edelsbrunner, Jacob E. Goodman, János Pach, Micha Sharir, Emo Welzl, and Günter M. Ziegler

    Discrete 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 Oct 05, 2014 11:20 AM PDT
  39. Program SGP: Mathematical Graphics

    Organizers: Bill Casselman and David Austin

    Please note, MSRI's Summer Graduate Programs are open only to students nominated by MSRI's Academic Sponsor universities.

    Updated on Jul 02, 2014 11:13 AM PDT
  40. Program Commutative Algebra

    Organizers: Luchezar Avramov, Mark Green, Craig Huneke, Karen E. Smith and Bernd Sturmfels

    Commutative 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 Oct 22, 2014 11:39 AM PDT
  41. Program Semi-Classical Analysis

    Organizers: Robert Littlejohn, William H. Miller, Johannes Sjorstrand, Steven Zelditch, and Maciej Zworski

    The traditional mathematical study of semi-classical 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 semi-classical analysis, in the new mathematics of "quantum chaos," and in physics and theoretical chemistry.

    Updated on Sep 30, 2014 12:40 AM PDT
  42. 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 Jul 03, 2014 04:41 PM PDT
  43. Program SGP: Biomathematics, Bioengineering & Clinical Aspects of Blood Flow

    Organizers: Stanley A. Berger, Giovanni P. Galdi (co-chair), Charles S. Peskin, Alfio Quarteroni, Anne M. Robertson (co-chair), Adélia Sequeira, and Howard Yonas

    Summer Graduate Program -- open only to students nominated by MSRI's Academic Sponsor universities.

    Updated on Jul 07, 2014 08:50 AM PDT
  44. Program Infinite-Dimensional Algebras and Mathematical Physics

    Organizers: E. Frenkel, V. Kac, I. Penkov, V. Serganova, G. Zuckerman

    This program will discuss recent progress in the representation theory of infinite-dimensional algebras and superalgebras and their applications to other fields.

    Updated on Oct 22, 2014 09:51 AM PDT
  45. Program Algebraic Stacks, Intersection Theory, and Non-Abelian Hodge Theory

    Organizers: W. Fulton, L. Katzarkov, M. Kontsevich, Y. Manin,R. Pandharipande, T. Pantev, C. Simpson and A. Vistoli

    Algebraic 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, non-abelian Hodge theory, string theory, etc. This program will focus on intersection theory on stacks, non-abelian Hodge theory and geometric n-stacks, perverse sheaves on stacks and the geometric Langlands program, D-brane charges in string theory, and moduli of gerbes and mirror symmetry.

    Updated on Oct 22, 2014 08:41 PM PDT
  46. Program Integral Geometry

    Organizers: L. Barchini, S. Gindikin, A. Goncharov and J. Wolf

    This 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 13-24

    Updated on Oct 22, 2014 07:44 AM PDT
  47. Program Inverse Problems

    Organizers: D. Colton, J. McLaughlin, W. Symes and G. Uhlmann

    In 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 non-destructive 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 13-24

    Updated on Aug 14, 2014 02:45 PM PDT
  48. Program SGP: Modern Signal Processing

    Organizers: Dan Rockmore and Dennis Healy

    MSRI'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 Aug 28, 2014 12:10 PM PDT
  49. Program Operator Algebras

    Organizers: C. Anantharaman-Delaroche, H. Araki, A. Connes, J. Cuntz, E.G. Effros, U. Haagerup, V.F.R. Jones , M.A. Rieffel and D.V. Voiculescu

    The noncommutative mathematics of operator algebras has grown in many directions and has made unexpected connections with other parts of mathematics and physics. Since the 1984-85 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 Oct 20, 2014 08:18 AM PDT
  50. Program Spectral Invariants

    Organizers: Tom Branson, S.-Y. Alice Chang, Rafe Mazzeo and Kate Okikiolu

    The 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 4-manifolds, index theory, relationship with scattering theory and other topics. This program will bring together people working on different problems in these areas.

    Updated on Sep 28, 2014 11:56 AM PDT
  51. Program Algorithmic Number Theory

    Organizers: Joe Buhler, Cynthia Dwork, Hendrik Lenstra Jr., Andrew Odlyzko, Bjorn Poonen and Noriko Yui

    Number 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 Oct 22, 2014 06:11 PM PDT
  52. Program SGP: Combinatorial Game Theory

    Organizers: E. Berlekamp, D. Wolfe

    SUMMER 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 Oct 03, 2014 12:03 PM PDT
  53. Program Noncommutative Algebra

    Organizers: Michael Artin, Susan Montgomery, Claudio Procesi, Lance Small, Toby Stafford, Efim Zelmanov

    For more information about this program, please see the original web page at:http://www.msri.org/activities/programs/9900/noncomm/index.html

    Updated on Sep 09, 2014 01:19 PM PDT
  54. Program SGP: Mathematical and Computational Challenges In Molecular and Cell Biology

    Organizers: Nicholas R. Cozzarelli, Michael Levitt, Wilma Olson, De Witt Sumners

    SUMMER 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 Jul 03, 2014 04:41 PM PDT
  55. Program Numerical and Applied Mathematics

    Organizers: Ivo Babuska, M. Vogelius, L. Wahlbin, R. Bank and D. Arnold

    For more information about this program, please see the original web page at:http://www.msri.org/activities/programs/9900/fem/index.html

    Updated on Jul 07, 2014 08:16 AM PDT
  56. Program Galois Groups and Fundamental Groups

    Organizers: Eva Bayer, Michael Fried, David Harbater, Yasutaka Ihara, B. Heinrich Matzat, Michel Raynaud, John Thompson

    For more information about this event, please see the original web page at:http://www.msri.org/activities/programs/9900/galois/index.html

    Updated on Oct 22, 2014 08:29 AM PDT
  57. Program SGP: Nonlinear dynamics of low-dimensional continua

    Organizers: L. Mahadevan and Anette Hosoi

    For more information, please see the original program page at http://www.msri.org/activities/events/9899/sgp99/mahadevan.html

    Updated on Jul 03, 2014 04:06 PM PDT
  58. Program Random Matrix Models and Their Applications

    Organizers: Pavel Bleher (co-Chair), Alan Edelman, Alexander Its (co-Chair), Craig Tracy and Harold Widom

    For 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 Sep 30, 2014 12:40 AM PDT
  59. Program Foundations of Computational Mathematics

    Organizers: Felipe Cucker (co-Chair), Arieh Iserles (co-Chair), Tien Yien Li, Mike Overton, Jim Renegar, Mike Shub (co-Chair), Steve Smale, and Andrew Stuart

    Please see the program's webpage at http://www.msri.org/activities/programs/9899/focm/index.html for more information.

    Updated on Jul 03, 2014 04:41 PM PDT
  60. Program Symbolic Computation in Geometry and Analysis

    Organizers: Marie-Francoise Roy, Michael Singer (Chair) and Bernd Sturmfels

    Please see the program webpage at http://www.msri.org/activities/programs/9899/symbcomp/index.html for more information.

    Updated on Oct 22, 2014 11:39 AM PDT
  61. Program Stochastic Analysis

    Organizers: R. Banuelos, S. Evans, P. Fitzsimmons, E. Pardoux, D. Stroock, and R. Williams

    Please see the program webpage at http://www.msri.org/activities/programs/9798/sa/index.html for more information.

    Updated on Sep 10, 2014 11:16 AM PDT
  62. Program Model Theory of Fields

    Organizers: Elisabeth Bouscaren, Lou van den Dries, Ehud Hrushovski, David Marker (co-Chair), Anand Pillay, Jose Felipe Voloch, and Carol Wood (co-Chair)

    Please see the program webpage at http://www.msri.org/activities/programs/9798/mtf/index.html for more information about this program.

    Updated on Oct 09, 2014 09:31 AM PDT
  63. 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 Oct 19, 2014 06:10 AM PDT
  64. Program Low-dimensional Topology

    Organizers: Joan Birman, Andrew Casson, Robion Kirby (Chair), and Ron Stern

    Please see the program webpage at http://www.msri.org/activities/programs/9697/ldt/index.html for more information.

    Updated on Oct 20, 2014 09:11 PM PDT
  65. Program SGP: Cryptography

    Organizers: Neal Koblitz, Alfred Menezes

    Updated on Sep 04, 2014 03:51 PM PDT
  66. 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 Oct 22, 2014 06:23 PM PDT
  67. Program Several Complex Variables

    Organizers: Jean-Pierre Demailly, Joseph J. Kohn, Junjiro Noguchi, Linda Rothschild, Michael Schneider, and Yum-Tong Siu (Chair)

    Please see the program webpage at http://www.msri.org/activities/programs/9596/scv/ for more information.

    Updated on Jul 03, 2014 04:41 PM PDT
  68. Program Holomorphic Spaces

    Organizers: Sheldon Axler (co-Chair), John McCarthy (co-Chair), Don Sarason (co-Chair), Joseph Ball, Nikolai Nikolskii, Mihai Putinar, and Cora Sadosky

    Please see the program webpage at http://www.msri.org/activities/programs/9596/hs/ for more information.

    Updated on Jul 03, 2014 04:41 PM PDT
  69. Program SGP: Random Walk and Geometry

    Organizers: Persi Diaconis, Laurent Saloff-Coste

    Updated on Oct 20, 2014 09:04 PM PDT
  70. Program Complex Dynamics and Hyperbolic Geometry

    Organizers: Bodil Branner, Steve Kerckhoff, Mikhail Lyubich, Curt McMullen (chair), and John Smillie

    Updated on Oct 21, 2014 08:22 AM PDT
  71. Program Automorphic Forms

    Organizers: Daniel Bump, Stephen Gelbart, Dennis Hejhal, Jeff Hoffstein (co-chairman), Steve Rallis (co-chairman), and Marie- France Vigneras

    Updated on Oct 22, 2014 09:21 AM PDT
  72. Program SGP: Hyperbolic Geometry

    Organizers: William P. Thurston, Jane Gilman, David Epstein

    Updated on Oct 20, 2014 09:04 PM PDT
  73. Program Dynamical Systems and Probabilistic Methods for PDE's

    Organizers: Percy Deift (co-chairman), Philip Holmes, James Hyman, David Levermore, David McLaughlin (co-chairman), Clarence Eugene Wayne

    Updated on Sep 09, 2014 03:36 PM PDT
  74. Program Differential Geometry

    Organizers: Werner Ballman, Raoul Bott, Carolyn Gordon, Mikhael Gromov, Karsten Grove, Blaine Lawson (chairman), Richard Schoen

    Updated on Oct 22, 2014 06:39 AM PDT
  75. Program Transcendence and Diophantine Problems

    Organizers: A. Baker (co-chairman), W. Brownawell, W. Schmidt (co- chairman), P. Vojta

    Updated on Sep 08, 2014 12:59 PM PDT
  76. Program Algebraic Geometry

    Organizers: E. Arbarello, A. Beauville, A. Beilinson, J. Harris, W. Fulton, J. Kollar, S. Mori, J. Steenbrink, H. Clemens & J. Kollar

    Updated on Oct 22, 2014 11:39 AM PDT
  77. Program Symbolic Dynamics

    Organizers: R. Adler (chairman), J. Franks, D. Lind, S. Williams

    Updated on Sep 12, 2014 10:18 AM PDT
  78. Program SGP: Mathematical Biology

    Organizers: N. Kopell, C. Peskin, M. Reed (chairman), J. Rinzel

    Created on May 29, 2005 02:19 AM PDT
  79. Program Statistics

    Organizers: P. Bickel (chairman), L. LeCam, D. Siegmund, T. Speed

    Updated on Aug 08, 2014 03:53 PM PDT
  80. Program Strings in Mathematics and Physics

    Organizers: O. Alvarez, D. Friedan, G. Moore, I.M. Singer (chairman), G. Segal, C. Taubes

    Updated on Sep 11, 2014 10:37 AM PDT
  81. Program SGP: 4-Manifolds

    Organizers: Rob Kirby, Ron Stern

    Updated on Jul 01, 2014 10:03 AM PDT
  82. Program Representations of Finite Groups

    Organizers: J. Alperin, C. Curtis (chairman), W. Feit, P. Fong

    Updated on Sep 08, 2014 09:49 AM PDT
  83. Program Logic

    Organizers: L. Harrington, A. Macintyre, D.A. Martin (chairman), R. Shore

    Updated on Oct 09, 2014 09:31 AM PDT
  84. Program Symplectic Geometry and Mechanics

    Organizers: R. Devaney, V. Guillemin (co-chairman), H. Flaschka, A. Weinstein (co-chairman)

    Updated on Aug 25, 2014 02:43 PM PDT
  85. Program Classical Analysis

    Organizers: C. Fefferman, E. Stein (chairman), G. Weiss

    Updated on Oct 13, 2014 02:10 PM PDT
  86. Program Representations of Lie Groups

    Organizers: W. Schmid, D. Vogan, J. Wolf (chairman)

    Updated on Oct 21, 2014 09:37 AM PDT
  87. Program Geometric Function Theory

    Organizers: D. Drasin, F. Gehring (chairman), I. Kra, A. Marden

    Updated on Sep 12, 2014 10:18 AM PDT
  88. Program Mathematical Economics

    Organizers: K. Arrow, G. Debreu (chairman), A. Mas-Colell

    Updated on Aug 11, 2014 06:14 AM PDT
  89. Program Computational Complexity

    Organizers: R. Graham, R. Karp (co-chairman), S. Smale (co-chairman)

    Updated on Sep 10, 2014 01:10 PM PDT
  90. Program Differential Geometry

    Organizers: S.-S. Chern (chairman), B. Lawson, I. M. Singer (miniprogram)

    Updated on Jul 01, 2014 10:17 AM PDT
  91. Program Low-dimensional Topology

    Organizers: R. Edwards (chairman), R. Kirby, J. Morgan, W. Thurston

    Updated on Oct 21, 2014 09:37 AM PDT
  92. Program Infinite-Dimensional Lie Algebras

    Organizers: H. Garland, I. Kaplansky (chairman), B. Kostant

    Updated on Sep 09, 2013 03:25 PM PDT
  93. Program Ergodic Theory and Dynamical Systems

    Organizers: J. Feldman (chairman), J. Franks, A. Katok, J. Moser, R. Temam

    Updated on Sep 29, 2014 03:45 PM PDT
  94. Program Mathematical Statistics

    Organizers: L. LeCam, D. Siegmund (chairman), C. Stone

    Updated on Jul 03, 2014 04:41 PM PDT