Acknowledged as the premier center for collaborative mathematical research, MSRI organizes and hosts semesterlength (or twosemesters duration) Programs that become the leading edge in that field of study. Mathematicians worldwide come to the Institute to engage in the research of classical fundamental mathematics, modern applied mathematics, statistics, computer science and other mathematical sciences. Upcoming MSRI Programs are listed as well as past Programs.

Complementary Program (201415)
Updated on Feb 27, 2014 09:09 AM PST 
Dynamics on Moduli Spaces of Geometric Structures
Organizers: Richard Canary (University of Michigan), William Goldman (University of Maryland), François Labourie (Université de Nice Sophia Antipolis), LEAD Howard Masur (University of Chicago), Anna Wienhard (RuprechtKarlsUniversität Heidelberg)The program will focus on the deformation theory of geometric structures on manifolds, and the resulting geometry and dynamics. This subject is formally a subfield of differential geometry and topology, with a heavy infusion of Lie theory. Its richness stems from close relations to dynamical systems, algebraic geometry, representation theory, Lie theory, partial differential equations, number theory, and complex analysis.
Updated on Apr 03, 2015 01:06 PM PDT 
Geometric and Arithmetic Aspects of Homogeneous Dynamics
Organizers: LEAD Dmitry Kleinbock (Brandeis University), Elon Lindenstrauss (Hebrew University), Hee Oh (Yale University), JeanFrançois Quint (Université de Bordeaux I), Alireza Salehi Golsefidy (University of California, San Diego)Homogeneous dynamics is the study of asymptotic properties of the action of subgroups of Lie groups on their homogeneous spaces. This includes many classical examples of dynamical systems, such as linear Anosov diffeomorphisms of tori and geodesic flows on negatively curved manifolds. This topic is related to many branches of mathematics, in particular, number theory and geometry. Some directions to be explored in this program include: measure rigidity of multidimensional diagonal groups; effectivization, sparse equidistribution and sieving; random walks, stationary measures and stiff actions; ergodic theory of thin groups; measure classification in positive characteristic. It is a companion program to “Dynamics on moduli spaces of geometric structures”.
Updated on Jan 12, 2015 10:58 AM PST

Summer Research
Created on Feb 23, 2015 04:41 PM PST 
New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems
Organizers: Kay Kirkpatrick (University of Illinois at UrbanaChampaign), Yvan Martel (École Polytechnique), Jonathan Mattingly (Duke University), Andrea Nahmod (University of Massachusetts, Amherst), Pierre Raphael (Universite de Nice SophiaAntipolis), Luc ReyBellet (University of Massachusetts, Amherst), LEAD Gigliola Staffilani (Massachusetts Institute of Technology), Daniel Tataru (University of California, Berkeley)The fundamental aim of this program is to bring together a core group of mathematicians from the general communities of nonlinear dispersive and stochastic partial differential equations whose research contains an underlying and unifying problem: quantitatively analyzing the dynamics of solutions arising from the flows generated by deterministic and nondeterministic evolution differential equations, or dynamical evolution of large physical systems, and in various regimes.
In recent years there has been spectacular progress within both communities in the understanding of this common problem. The main efforts exercised, so far mostly in parallel, have generated an incredible number of deep results, that are not just beautiful mathematically, but are also important to understand the complex natural phenomena around us. Yet, many open questions and challenges remain ahead of us. Hosting the proposed program at MSRI would be the most effective venue to explore the specific questions at the core of the unifying theme and to have a focused and open exchange of ideas, connections and mathematical tools leading to potential new paradigms. This special program will undoubtedly produce new and fundamental results in both areas, and possibly be the start of a new generation of researchers comfortable on both languages.
Updated on Apr 03, 2015 01:05 PM PDT 
Complementary Program
Updated on Jan 26, 2015 04:20 PM PST 
Differential Geometry
Organizers: Tobias Colding (Massachusetts Institute of Technology), Simon Donaldson (Imperial College, London), John Lott (University of California, Berkeley), Natasa Sesum (Rutgers University), Gang Tian (Princeton University), LEAD Jeff Viaclovsky (University of Wisconsin)Differential geometry is a subject with both deep roots and recent advances. Many old problems in the field have recently been solved, such as the Poincaré and geometrization conjectures by Perelman, the quarter pinching conjecture by BrendleSchoen, the Lawson Conjecture by Brendle, and the Willmore Conjecture by MarquesNeves. The solutions of these problems have introduced a wealth of new techniques into the field. This semesterlong program will focus on the following main themes:
(1) Einstein metrics and generalizations,
(2) Complex differential geometry,
(3) Spaces with curvature bounded from below,
(4) Geometric flows,
and particularly on the deep connections between these areas.Updated on Apr 21, 2015 03:40 PM PDT 
Geometric Group Theory
Organizers: Ian Agol (University of California, Berkeley), Mladen Bestvina (University of Utah), Cornelia Drutu (University of Oxford), LEAD Mark Feighn (Rutgers University), Michah Sageev (TechnionIsrael Institute of Technology), Karen Vogtmann (Cornell University)The field of geometric group theory emerged from Gromov’s insight that even mathematical objects such as groups, which are defined completely in algebraic terms, can be profitably viewed as geometric objects and studied with geometric techniques Contemporary geometric group theory has broadened its scope considerably, but retains this basic philosophy of reformulating in geometric terms problems from diverse areas of mathematics and then solving them with a variety of tools. The growing list of areas where this general approach has been successful includes
lowdimensional topology, the theory of manifolds, algebraic topology, complex dynamics, combinatorial group theory, algebra, logic, the study of various classical families of groups, Riemannian geometry and representation theory.
The goals of this MSRI program are to bring together people from the various branches of the field in order to consolidate recent progress, chart new directions, and train the next generation of geometric group theorists.Updated on Oct 11, 2013 02:11 PM PDT 
Analytic Number Theory
Organizers: Chantal David (Concordia University), Andrew Granville (Université de Montréal), Emmanuel Kowalski (Eidgenössische TH ZürichHönggerberg), Philippe Michel, Kannan Soundararajan (Stanford University), LEAD Terence Tao (University of California, Los Angeles)Analytic number theory, and its applications and interactions, are currently experiencing intensive progress, in sometimes unexpected directions. In recent years, many important classical questions have seen spectacular advances based on new techniques; conversely, methods developed in analytic number theory have led to the solution of striking problems in other fields.
This program will not only give the leading researchers in the area further opportunities to work together, but more importantly give young people the occasion to learn about these topics, and to give them the tools to achieve the next breakthroughs.
Updated on Apr 13, 2015 10:51 AM PDT 
Harmonic Analysis
Organizers: LEAD Michael Christ (University of California, Berkeley), Allan Greenleaf (University of Rochester), Steven Hofmann (University of Missouri), LEAD Michael Lacey (Georgia Institute of Technology), Svitlana Mayboroda (University of Minnesota, Twin Cities), Betsy Stovall (University of Wisconsin), Brian Street (University of Wisconsin)Updated on Apr 15, 2015 02:03 PM PDT 
Geometric Functional Analysis and Applications
Organizers: Franck Barthe, Marianna Csornyei (University College), Boaz Klartag, Alexander Koldobsky, Rafal Latala, LEAD Mark RudelsonUpdated on Apr 03, 2015 01:18 PM PDT 
Group Representation Theory and Applications
Organizers: Robert Guralnick (University of Southern California), Alexander (Sasha) Kleshchev (University of Oregon), Gunter Malle (Universität Kaiserslautern), Gabriel Navarro (University of Valencia), Julia Pevtsova (University of Washington), Raphael Rouquier (University of California, Los Angeles), LEAD Pham Tiep (University of Arizona)Group Representation Theory is a central area of Algebra, with important and deep connections to areas as varied as topology, algebraic geometry, number theory, Lie theory, homological algebra, and mathematical physics. Born more than a century ago, the area still abounds with basic problems and fundamental conjectures, some of which have been open for over five decades. Very recent breakthroughs have led to the hope that some of these conjectures can finally be settled. In turn, recent results in group representation theory have helped achieve substantial progress in a vast number of applications.
The goal of the program is to investigate all these deep problems and the wealth of new results and directions, to obtain major progress in the area, and to explore further applications of group representation theory to other branches of mathematics.
Updated on Apr 10, 2015 02:52 PM PDT
Past Programs

Program Geometric Representation Theory
Organizers: LEAD David BenZvi (University of Texas), Ngô Bảo Châu (University of Chicago), Thomas Haines (University of Maryland), Florian Herzig (University of Toronto), Kevin McGerty (University of Oxford), David Nadler (University of California, Berkeley), Catharina Stroppel (Hausdorff Research Institute for Mathematics, University of Bonn), Eva Viehmann (TU München)The fundamental aims of geometric representation theory are to uncover the deeper geometric and categorical structures underlying the familiar objects of representation theory and harmonic analysis, and to apply the resulting insights to the resolution of classical problems. One of the main sources of inspiration for the field is the Langlands philosophy, a vast nonabelian generalization of the Fourier transform of classical harmonic analysis, which serves as a visionary roadmap for the subject and places it at the heart of number theory. A primary goal of the proposed MSRI program is to explore the potential impact of geometric methods and ideas in the Langlands program by bringing together researchers working in the diverse areas impacted by the Langlands philosophy, with a particular emphasis on representation theory over local fields.
Another focus comes from theoretical physics, where new perspectives on the central objects of geometric representation theory arise in the study supersymmetric gauge theory, integrable systems and topological string theory. The impact of these ideas is only beginning to be absorbed and the program will provide a forum for their dissemination and development.
Updated on Aug 13, 2014 09:08 AM PDT 
Program New Geometric Methods in Number Theory and Automorphic Forms
Organizers: Pierre Colmez (Institut de Mathématiques de Jussieu), LEAD Wee Teck Gan (National University of Singapore), Michael Harris (Institut de Mathématiques de Jussieu), Elena Mantovan (California Institute of Technology), Ariane Mézard (Institut de Mathématiques de Jussieu), Akshay Venkatesh (Stanford University)The branches of number theory most directly related to the arithmetic of automorphic forms have seen much recent progress, with the resolution of many longstanding conjectures. These breakthroughs have largely been achieved by the discovery of new geometric techniques and insights. The goal of this program is to highlight new geometric structures and new questions of a geometric nature which seem most crucial for further development. In particular, the program will emphasize geometric questions arising in the study of Shimura varieties, the padic Langlands program, and periods of automorphic forms.
Updated on Oct 11, 2013 02:02 PM PDT 
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 ominimality. Current areas of lively interaction include motivic integration, valued fields, diophantine geometry, and algebraic dynamics.
Updated on Feb 19, 2014 02:02 PM PST 
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 
Program Mathematical General Relativity
Organizers: Yvonne ChoquetBruhat, 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 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 Apr 24, 2015 01:57 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 26, 2015 04:36 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 Mar 30, 2015 03:28 PM PDT 
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 08, 2015 10:45 AM 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 Mar 24, 2015 03:02 PM PDT 
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 Apr 19, 2015 07:39 AM PDT 
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 19, 2014 09:30 PM 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 08, 2015 04:01 PM 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 13, 2015 03:44 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 22, 2015 10:07 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 24, 2015 05:34 AM 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 24, 2015 01:57 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 Jan 09, 2015 11:38 AM PST 
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, 2015 07:13 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 27, 2015 03:33 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 28, 2015 12:15 AM 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 24, 2015 08:50 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 07, 2015 02:09 PM PDT 
Program Computational Applications of Algebraic Topology
Organizers: Gunnar Carlsson, Persi Diaconis, Susan Holmes, Rick Jardine, Günter M. ZieglerUpdated on Mar 13, 2015 03:44 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 20, 2015 10:35 AM PDT