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Past Programs

  1. Program Universality and Integrability in Random Matrix Theory and Interacting Particle Systems

    Organizers: LEAD Ivan Corwin (Columbia University), Percy Deift (New York University, Courant Institute), Ioana Dumitriu (University of California, San Diego), Alice Guionnet (École Normale Supérieure de Lyon), Alexander Its (Indiana University--Purdue University), Herbert Spohn (Technische Universität München), Horng-Tzer Yau (Harvard University)

    The past decade has seen tremendous progress in understanding the behavior of large random matrices and interacting particle systems. Complementary methods have emerged to prove universality of these behaviors, as well as to probe their precise nature using integrable, or exactly solvable models. This program seeks to reinforce and expand the fruitful interaction at the interface of these areas, as well as to showcase some of the important developments and applications of the past decade.

    Updated on Aug 31, 2021 03:05 PM PDT
  2. Program Complementary Program 2020-21

    The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program.

    Updated on Jul 14, 2021 09:02 AM PDT
  3. Program Mathematical problems in fluid dynamics

    Organizers: Thomas Alazard (Ecole Normale Supérieure Paris-Saclay; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Laboratoire Jacques-Louis Lions; Centre National de la Recherche Scientifique (CNRS)), Mihaela Ifrim (University of Wisconsin-Madison), Igor Kukavica (University of Southern California), David Lannes (Institut de Mathématiques de Bordeaux; Centre National de la Recherche Scientifique (CNRS)), LEAD Daniel Tataru (University of California, Berkeley)

    All scientific activities in this program will be available online so that those who can't attend in person are able to participate. If you are not a member of the program and would like to participate in any of the online activities, please fill out this REGISTRATION FORM.


    Fluid dynamics is one of the classical areas of partial differential equations, and has been the subject of extensive research over hundreds of years. It is perhaps one of the most challenging and exciting fields of scientific pursuit simply because of the complexity of the subject and the endless breadth of applications.

    The focus of the program is on incompressible fluids, where water is a primary example. The fundamental equations in this area are the well-known Euler equations for inviscid fluids, and the Navier-Stokes equations for the viscous fluids. Relating the two is the problem of the zero viscosity limit, and its connection to the phenomena of turbulence. Water waves, or more generally interface problems in fluids, represent another target area for the program. Both theoretical and numerical aspects will be considered.

    Updated on Mar 16, 2021 02:28 PM PDT
  4. Program Random and Arithmetic Structures in Topology -- Virtual Semester

    Organizers: Nicolas Bergeron (École Normale Supérieure), Jeffrey Brock (Yale University), Alexander Furman (University of Illinois at Chicago), Tsachik Gelander (Weizmann Institute of Science), Ursula Hamenstädt (Rheinische Friedrich-Wilhelms-Universität Bonn), Fanny Kassel (Institut des Hautes Études Scientifiques (IHES)), LEAD Alan Reid (Rice University)
    Msri image

    Until further notice, the MSRI building will only be open to a small group of essential staff and members of the Fall 2020 scientific programs.

    All scientific activities in this program will be available online so that those who can't attend in person are able to participate. If you are not a member of the program and would like to participate in any of the online activities, please fill out this REGISTRATION FORM.

    Updated on Sep 21, 2020 04:57 PM PDT
  5. Program Decidability, definability and computability in number theory: Part 1 - Virtual Semester

    Organizers: LEAD Valentina Harizanov (George Washington University), Maryanthe Malliaris (University of Chicago), Barry Mazur (Harvard University), Russell Miller (Queens College, CUNY; CUNY, Graduate Center), Jonathan Pila (University of Oxford), Thomas Scanlon (University of California, Berkeley), LEAD Alexandra Shlapentokh (East Carolina University), Carlos Videla (Mount Royal University)
    Image edited
    Title page of Diophantus' Arithmetica - ETH Zurich

    Until further notice, the MSRI building will only be open to a small group of essential staff and members of the Fall 2020 scientific programs.

    All scientific activities in this program will be available online so that those who can't attend in person are able to participate. If you are not a member of the program and would like to participate in any of the online activities, please fill out this REGISTRATION FORM.

    Updated on Oct 29, 2020 10:47 AM PDT
  6. Program Quantum Symmetries

    Organizers: Vaughan Jones (Vanderbilt University), LEAD Scott Morrison (Australian National University), Victor Ostrik (University of Oregon), Emily Peters (Loyola University), Eric Rowell (Texas A & M University), LEAD Noah Snyder (Indiana University), Chelsea Walton (Rice University)
    Program picture
    The study of tensor categories involves the interplay of representation theory, combinatorics, number theory, and low dimensional topology (from a string diagram calculation, describing the 3-dimensional bordism 2-category [arXiv:1411.0945]).

    Symmetry, as formalized by group theory, is ubiquitous across mathematics and science. Classical examples include point groups in crystallography, Noether's theorem relating differentiable symmetries and conserved quantities, and the classification of fundamental particles according to irreducible representations of the Poincaré group and the internal symmetry groups of the standard model. However, in some quantum settings, the notion of a group is no longer enough to capture all symmetries. Important motivating examples include Galois-like symmetries of von Neumann algebras, anyonic particles in condensed matter physics, and deformations of universal enveloping algebras. The language of tensor categories provides a unified framework to discuss these notions of quantum symmetry.

    Updated on Jan 14, 2020 02:21 PM PST
  7. Program Higher Categories and Categorification

    Organizers: David Ayala (Montana State University), Clark Barwick (University of Edinburgh), David Nadler (University of California, Berkeley), LEAD Emily Riehl (Johns Hopkins University), Marcy Robertson (University of Melbourne), Peter Teichner (Max-Planck-Institut für Mathematik), Dominic Verity (Macquarie University)
    Higher adjunction axiom
    swallowtail identity

    Though many of the ideas in higher category theory find their origins in homotopy theory — for instance as expressed by Grothendieck’s “homotopy hypothesis” — the subject today interacts with a broad spectrum of areas of mathematical research. Unforeseen descent, or local-to-global formulas, for familiar objects can be articulated in terms of higher invertible morphisms. Compatible associative deformations of a sequence of maps of spaces, or derived schemes, can putatively be represented by higher categories, as Koszul duality for E_n-algebras suggests. Higher categories offer unforeseen characterizing universal properties for familiar constructions such as K-theory. Manifold theory is natively connected to higher category theory and adjunction data, a connection that is most famously articulated by the recently proven Cobordism Hypothesis.
    In parallel, the idea of "categorification'' is playing an increasing role in algebraic geometry, representation theory, mathematical physics, and manifold theory, and higher categorical structures also appear in the very foundations of mathematics in the form of univalent foundations and homotopy type theory. A central mission of this semester will be to mitigate the exorbitantly high "cost of admission'' for mathematicians in other areas of research who aim to apply higher categorical technology and to create opportunities for potent collaborations between mathematicians from these different fields and experts from within higher category theory.

    Updated on Jan 10, 2020 03:55 PM PST
  8. Program Complementary Program 2019-20

    The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program. 

    Updated on Nov 27, 2018 12:28 PM PST
  9. Program Holomorphic Differentials in Mathematics and Physics

    Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at Urbana-Champaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (Yale University), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg), Anton Zorich (Institut de Mathematiques de Jussieu)
    Some holomorphic differentials on a genus 2 surface, with close up views of singular points, image courtesy Jian Jiang.

    Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special - Hitchin or higher Teichmuller - components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).

    It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our program will be of interest to those working in many different elds, including low-dimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).

    Updated on Dec 13, 2019 10:03 AM PST
  10. Program Microlocal Analysis

    Organizers: Pierre Albin (University of Illinois at Urbana-Champaign), Nalini Anantharaman (Université de Strasbourg), Kiril Datchev (Purdue University), Raluca Felea (Rochester Institute of Technology), Colin Guillarmou (Université Paris-Saclay), LEAD Andras Vasy (Stanford University)
    315 image1

    Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This program will bring together researchers from various parts of the field to facilitate the transfer of ideas, and will also provide a comprehensive introduction to the field for postdocs and graduate students.

    Updated on Apr 13, 2018 11:42 AM PDT
  11. Program Complementary Program 2018-19

    The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program. 

    Updated on Jun 03, 2019 10:25 AM PDT
  12. Program Derived Algebraic Geometry

    Organizers: Julie Bergner (University of Virginia), LEAD Bhargav Bhatt (University of Michigan), Dennis Gaitsgory (Harvard University), David Nadler (University of California, Berkeley), Nick Rozenblyum (University of Chicago), Peter Scholze (Universität Bonn), Gabriele Vezzosi (Università di Firenze)
    Courtesy of G. Karapet

    Derived algebraic geometry is an extension of algebraic geometry that provides a convenient framework for directly treating non-generic geometric situations (such as non-transverse intersections in intersection theory), in lieu of the more traditional perturbative approaches (such as the “moving” lemma). This direct approach, in addition to being conceptually satisfying, has the distinct advantage of preserving the symmetries of the situation, which makes it much more applicable. In particular, in recent years, such techniques have found applications in diverse areas of mathematics, ranging from arithmetic geometry, mathematical physics, geometric representation theory, and homotopy theory. This semester long program will be dedicated to exploring these directions further, and finding new connections.

    Updated on Jan 02, 2019 03:00 PM PST
  13. Program Birational Geometry and Moduli Spaces

    Organizers: Antonella Grassi (University of Pennsylvania), LEAD Christopher Hacon (University of Utah), Sándor Kovács (University of Washington), Mircea Mustaţă (University of Michigan), Martin Olsson (University of California, Berkeley)

    Birational Geometry and Moduli Spaces are two important areas of Algebraic Geometry that have recently witnessed a flurry of activity and substantial progress on many fundamental open questions. In this program we aim to  bring together key researchers in these and related areas to highlight the recent exciting progress and to explore future avenues of research.
    This program will focus on the following themes: Geometry and Derived Categories, Birational Algebraic Geometry, Moduli Spaces of Stable Varieties, Geometry in Characteristic p>0, and Applications of Algebraic Geometry: Elliptic Fibrations of Calabi-Yau Varieties in Geometry, Arithmetic and the Physics of String Theory

    Updated on Jan 31, 2017 07:46 PM PST
  14. Program Hamiltonian systems, from topology to applications through analysis

    Organizers: Rafael de la Llave (Georgia Institute of Technology), LEAD Albert Fathi (Georgia Institute of Technology; École Normale Supérieure de Lyon), vadim kaloshin (University of Maryland), Robert Littlejohn (University of California, Berkeley), Philip Morrison (University of Texas, Austin), Tere Seara (Polytechnical University of Cataluña (Barcelona)), Sergei Tabachnikov (Pennsylvania State University), Amie Wilkinson (University of Chicago)

    The interdisciplinary nature of Hamiltonian systems is deeply ingrained in its history. Therefore the program will bring together the communities of mathematicians with the community of practitioners, mainly engineers, physicists, and theoretical chemists who use Hamiltonian systems daily. The program will cover not only the mathematical aspects of Hamiltonian systems but also their applications, mainly in space mechanics, physics and chemistry.

    The mathematical aspects comprise celestial mechanics, variational methods, relations with PDE, Arnold diffusion and computation. The applications concern celestial mechanics, astrodynamics, motion of satellites, plasma physics, accelerator physics, theoretical chemistry, and atomic physics.

    The goal of the program is to bring to the forefront both the theoretical aspects and the applications, by making available for applications the latest theoretical developments, and also by nurturing the theoretical mathematical aspects with new problems that come from concrete problems of applications.

    Updated on Aug 20, 2018 08:16 AM PDT
  15. Program Summer Research for Women in Mathematics

    Organizers: Hélène Barcelo (MSRI - Mathematical Sciences Research Institute)

    See this LINK for the 2019 Summer Research for Women in Mathematics program.
    The purpose of the MSRI's program, Summer Research for Women in Mathematics, is to provide space and funds to groups of women mathematicians to work on a research project at MSRI. Research projects can arise from work initiated at a Women's Conference, or can be freestanding activities.

    Updated on Sep 11, 2018 01:32 PM PDT
  16. Program Group Representation Theory and Applications

    Organizers: Robert Guralnick (University of Southern California), Alexander 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 (Rutgers University)

    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 Jan 12, 2018 04:00 PM PST
  17. Program Enumerative Geometry Beyond Numbers

    Organizers: Mina Aganagic (University of California, Berkeley), Denis Auroux (University of California, Berkeley), Jim Bryan (University of British Columbia), LEAD Andrei Okounkov (Columbia University), Balazs Szendroi (University of Oxford)

    Traditional enumerative geometry asks certain questions to which the expected answer is a number: for instance, the number of lines incident with two points in the plane (1, Euclid), or the number of twisted cubic curves on a quintic threefold (317 206 375). It has however been recognized for some time that the numerics is often just the tip of the iceberg: a deeper exploration reveals interesting geometric, topological, representation-, or knot-theoretic structures. This semester-long program will be devoted to these hidden structures behind enumerative invariants, concentrating on the core fields where these questions start: algebraic and symplectic geometry.

    Updated on Jan 16, 2018 10:12 AM PST
  18. Program Geometric Functional Analysis and Applications

    Organizers: Franck Barthe (Université de Toulouse III (Paul Sabatier)), Marianna Csornyei (University of Chicago), Boaz Klartag (Weizmann Institute of Science), Alexander Koldobsky (University of Missouri), Rafal Latala (University of Warsaw), LEAD Mark Rudelson (University of Michigan)

    Geometric functional analysis lies at the interface of convex geometry, functional analysis and probability. It has numerous applications ranging from geometry of numbers and random matrices in pure mathematics to geometric tomography and signal processing in engineering and numerical optimization and learning theory in computer science.

    One of the directions of the program is classical convex geometry, with emphasis on connections with geometric tomography, the study of geometric properties of convex bodies based on information about their sections and projections. Methods of harmonic analysis play an important role here. A closely related direction is asymptotic geometric analysis studying geometric properties of high dimensional objects and normed spaces, especially asymptotics of their quantitative parameters as dimension tends to infinity. The main tools here are concentration of measure and related probabilistic results. Ideas developed in geometric functional analysis have led to progress in several areas of applied mathematics and computer science, including compressed sensing and random matrix methods. These applications as well as the problems coming from computer science will be also emphasised in our program.

    Updated on Aug 23, 2017 03:38 PM PDT
  19. Program Geometric and Topological Combinatorics

    Organizers: Jesus De Loera (University of California, Davis), Victor Reiner (University of Minnesota Twin Cities), LEAD Francisco Santos Leal (University of Cantabria), Francis Su (Harvey Mudd College), Rekha Thomas (University of Washington), Günter Ziegler (Freie Universität Berlin)

    Combinatorics is one of the fastest growing areas in contemporary Mathematics, and much of this growth is due to the connections and interactions with other areas of Mathematics. This program is devoted to the very vibrant and active area of interaction between Combinatorics with Geometry and Topology. That is, we focus on (1) the study of the combinatorial properties or structure of geometric and topological objects and (2) the development of geometric and topological techniques to answer combinatorial problems.

    Key examples of geometric objects with intricate combinatorial structure are point configurations and matroids, hyperplane and subspace arrangements, polytopes and polyhedra, lattices, convex bodies, and sphere packings. Examples of topology in action answering combinatorial challenges are the by now classical Lovász’s solution of the Kneser conjecture, which yielded functorial approaches to graph coloring, and the  more recent, extensive topological machinery leading to breakthroughs on Tverberg-type problems.

    Updated on Aug 28, 2017 11:26 AM PDT
  20. Program Summer Research 2017

    Come spend time at MSRI in the summer! The Institute’s summer graduate schools and undergraduate program fill the lecture halls and some of the offices, but we have room for a modest number of visitors to come to do research singly or in small groups, while enjoying the excellent mathematical facilities, the great cultural opportunities of Berkeley, San Francisco and the Bay area, the gorgeous natural surroundings, and the cool weather.

    We can provide offices, library facilities and bus passes—unfortunately not financial support. Though the auditoria are largely occupied, there are blackboards and ends of halls, so 2-6 people could comfortably collaborate with one another. We especially encourage such groups to apply together.

    To make visits productive, we require at least a two-week commitment.  We strive for a wide mix of people, being sure to give special consideration to women, under-represented groups, and researchers from non-research universities. 

    Updated on May 31, 2018 12:40 PM PDT
  21. Program Complementary Program (2016-17)

    The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program. 

    Updated on Apr 14, 2017 10:04 AM PDT
  22. Program Analytic Number Theory

    Organizers: Chantal David (Concordia University), Andrew Granville (Université de Montréal), Emmanuel Kowalski (ETH Zurich), Philippe Michel (École Polytechnique Fédérale de Lausanne (EPFL)), 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 Jul 10, 2015 03:54 PM PDT
  23. Program 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-Madison), Brian Street (University of Wisconsin-Madison)

    The field of Harmonic Analysis dates back to the 19th century, and has its roots in the study of the decomposition of functions using Fourier series and the Fourier transform.  In recent decades, the subject has undergone a rapid diversification and expansion, though the decomposition of functions and operators into simpler parts remains a central tool and theme.  
    This program will bring together researchers representing the breadth of modern Harmonic Analysis and will seek to capitalize on and continue recent progress in four major directions:
         -Restriction, Kakeya, and Geometric Incidence Problems
         -Analysis on Nonhomogeneous Spaces
         -Weighted Norm Inequalities
         -Quantitative Rectifiability and Elliptic PDE.
    Many of these areas draw techniques from or have applications to other fields of mathematics, such as analytic number theory, partial differential equations, combinatorics, and geometric measure theory.  In particular, we expect a lively interaction with the concurrent program.  

    Updated on Aug 11, 2016 10:49 AM PDT
  24. Program 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 (Technion---Israel Institute of Technology), Karen Vogtmann (University of Warwick)

    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 low-dimensional 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 Aug 11, 2016 08:44 AM PDT
  25. Program Summer Research 2016

    Come spend time at MSRI in the summer! The Institute’s summer graduate schools and undergraduate program fill the lecture halls and some of the offices, but we have room for a modest number of visitors to come to do research singly or in small groups, while enjoying the excellent mathematical facilities, the great cultural opportunities of Berkeley, San Francisco and the Bay area, the gorgeous natural surroundings, and the cool weather.

    We can provide offices, library facilities and bus passes—unfortunately not financial support. Though the auditoria are largely occupied, there are blackboards and ends of halls, so 2-6 people could comfortably collaborate with one another. We especially encourage such groups to apply together.

    To make visits productive, we require at least a two-week commitment.  We strive for a wide mix of people, being sure to give special consideration to women, under-represented groups, and researchers from non-research universities.  

    Updated on Mar 22, 2016 11:58 AM PDT
  26. Program Differential Geometry

    Organizers: Tobias Colding (Massachusetts Institute of Technology), Simon Donaldson (State University of New York, Stony Brook), John Lott (University of California, Berkeley), Natasa Sesum (Rutgers University), Gang Tian (Princeton University), LEAD Jeff Viaclovsky (University of Wisconsin-Madison)

    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 Brendle-Schoen, the Lawson Conjecture by Brendle, and the Willmore Conjecture by Marques-Neves. The solutions of these problems have introduced a wealth of new techniques into the field. This semester-long 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 Oct 17, 2019 02:16 PM PDT
  27. Program New Challenges in PDE: Deterministic Dynamics and Randomness in High and Infinite Dimensional Systems

    Organizers: Kay Kirkpatrick (University of Illinois at Urbana-Champaign), Yvan Martel (École Polytechnique), Jonathan Mattingly (Duke University), Andrea Nahmod (University of Massachusetts, Amherst), Pierre Raphael (Université Nice Sophia-Antipolis), Luc Rey-Bellet (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 non-deterministic 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 Sep 15, 2015 05:25 PM PDT
  28. Program Summer Research

    Come spend time at MSRI in the summer! The Institute’s summer graduate schools and undergraduate program fill the lecture halls and some of the offices, but we have room for a modest number of visitors to come to do research singly or in small groups, while enjoying the excellent mathematical facilities, the great cultural opportunities of Berkeley, San Francisco and the Bay area, the gorgeous natural surroundings, and the cool weather.

    We can provide offices, library facilities and bus passes—unfortunately not financial support. Though the auditoria are largely occupied, there are blackboards and ends of halls, so 2-6 people could comfortably collaborate with one another. We especially encourage such groups to apply together.

    To make visits productive, we require at least a two-week commitment.  We strive for a wide mix of people, being sure to give special consideration to women, under-represented groups, and researchers from non-research universities.  

    Updated on May 06, 2015 11:36 AM PDT
  29. Program Geometric and Arithmetic Aspects of Homogeneous Dynamics

    Organizers: LEAD Dmitry Kleinbock (Brandeis University), Elon Lindenstrauss (The Hebrew University of Jerusalem), Hee Oh (Yale University), Jean-François 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
  30. Program Dynamics on Moduli Spaces of Geometric Structures

    Organizers: Richard Canary (University of Michigan), William Goldman (University of Maryland), François Labourie (Universite de Nice Sophia Antipolis), LEAD Howard Masur (University of Chicago), Anna Wienhard (Ruprecht-Karls-Universität 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
  31. Program Geometric Representation Theory

    Organizers: LEAD David Ben-Zvi (University of Texas, Austin), 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 (Rheinische Friedrich-Wilhelms-Universität 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 Oct 17, 2019 01:13 PM PDT
  32. 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 (Columbia University), Elena Mantovan (California Institute of Technology), Ariane Mézard (Institut de Mathématiques de Jussieu; École Normale Supérieure), Akshay Venkatesh (Institute for Advanced Study)

    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 p-adic Langlands program, and periods of automorphic forms.

    Updated on Oct 11, 2013 02:02 PM PDT
  33. Program Model Theory, Arithmetic Geometry and Number Theory

    Organizers: Ehud Hrushovski (The Hebrew University of Jerusalem), François Loeser (Université de Paris VI (Pierre et Marie Curie)), David Marker (University of Illinois, Chicago), 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 May 01, 2019 02:07 PM PDT
  34. Program Algebraic Topology

    Organizers: Vigleik Angeltveit (Australian National University), Andrew Blumberg (Columbia University), Gunnar Carlsson (Stanford University), Teena Gerhardt (Michigan State University), LEAD Michael Hill (University of California, Los Angeles), 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 Oct 17, 2019 01:05 PM PDT
  35. 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 (Princeton University), Richard Schoen (University of California, Irvine)

    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 May 01, 2019 01:14 PM PDT
  36. 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, Austin), Wilfrid Gangbo (University of California, Los Angeles), 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 Oct 17, 2019 01:04 PM PDT
  37. 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
  38. 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
  39. 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
  40. 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 Aug 10, 2015 02:30 PM PDT
  41. 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 17, 2019 02:39 PM PDT
  42. 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 Oct 17, 2019 01:42 PM PDT
  43. 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 17, 2019 02:19 PM PDT
  44. 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 Oct 17, 2019 01:08 PM PDT
  45. 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 May 17, 2022 09:02 AM PDT
  46. 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 May 19, 2022 07:36 AM PDT
  47. 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
  48. 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 Feb 08, 2022 10:39 PM PST
  49. 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 May 18, 2022 09:13 AM PDT
  50. 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 May 13, 2022 06:23 PM PDT
  51. 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 Feb 11, 2022 03:36 PM PST
  52. 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 Feb 11, 2022 03:43 PM PST
  53. 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 May 02, 2022 09:33 AM PDT
  54. 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 Dec 23, 2021 08:37 AM PST
  55. 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 May 17, 2022 09:02 AM PDT
  56. 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 Feb 18, 2022 03:40 PM PST
  57. 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 Apr 22, 2022 09:23 AM PDT
  58. 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 May 04, 2022 10:51 AM PDT
  59. 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 Apr 12, 2022 09:03 AM PDT
  60. 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 May 04, 2022 10:12 AM PDT
  61. 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 May 08, 2022 10:19 AM PDT
  62. 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 Feb 11, 2022 03:29 PM PST
  63. 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 Feb 23, 2022 12:33 PM PST
  64. 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 Apr 28, 2022 10:43 AM PDT
  65. 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 May 17, 2022 09:02 AM PDT
  66. 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 May 19, 2022 01:40 PM PDT
  67. 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 Mar 16, 2022 02:22 PM PDT
  68. 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 Feb 16, 2022 03:04 PM PST
  69. 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 Apr 28, 2022 10:43 AM PDT
  70. 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 Aug 19, 2021 12:44 PM PDT
  71. 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 May 02, 2022 09:33 AM PDT
  72. 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 Apr 13, 2022 03:46 PM PDT
  73. 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 Feb 16, 2022 08:49 AM PST
  74. 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 May 13, 2022 06:23 PM PDT
  75. 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 Sep 09, 2021 02:50 PM PDT
  76. 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 May 13, 2022 06:23 PM PDT
  77. 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 May 02, 2022 12:13 PM PDT
  78. 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 May 02, 2022 09:33 AM PDT
  79. 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 Apr 21, 2022 03:31 PM PDT
  80. 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 May 19, 2022 01:40 PM PDT
  81. 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 Feb 11, 2022 04:14 PM PST
  82. 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 Feb 21, 2022 12:44 PM PST
  83. 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 Mar 17, 2022 05:39 PM PDT
  84. 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 May 02, 2022 12:13 PM PDT
  85. 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 Apr 12, 2022 01:50 PM PDT
  86. 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 08, 2022 10:13 AM PST
  87. 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 May 17, 2022 09:03 AM PDT
  88. 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 May 02, 2022 09:33 AM PDT
  89. 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 May 19, 2022 01:40 PM PDT
  90. 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 May 12, 2022 08:06 AM PDT
  91. Program Complex Dynamics and Hyperbolic Geometry

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

    Updated on May 17, 2022 09:02 AM PDT
  92. Program Automorphic Forms

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

    Updated on Apr 29, 2022 10:27 AM PDT
  93. 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 May 08, 2022 10:19 AM PDT
  94. Program Differential Geometry

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

    Updated on May 13, 2022 06:23 PM PDT
  95. Program Transcendence and Diophantine Problems

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

    Updated on Feb 28, 2022 01:14 PM PST
  96. 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 Apr 14, 2022 09:13 AM PDT
  97. Program Symbolic Dynamics

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

    Updated on May 07, 2022 11:05 AM PDT
  98. Program Statistics

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

    Updated on Feb 19, 2022 10:04 AM PST
  99. Program Strings in Mathematics and Physics

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

    Updated on Feb 11, 2022 04:11 PM PST
  100. Program Representations of Finite Groups

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

    Updated on Feb 11, 2022 04:00 PM PST
  101. Program Logic

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

    Updated on May 02, 2022 12:13 PM PDT
  102. Program Symplectic Geometry and Mechanics

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

    Updated on Apr 14, 2022 01:53 PM PDT
  103. Program Classical Analysis

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

    Updated on Mar 01, 2022 05:39 AM PST
  104. Program Representations of Lie Groups

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

    Updated on Oct 11, 2021 03:13 PM PDT
  105. Program Geometric Function Theory

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

    Updated on May 17, 2022 09:02 AM PDT
  106. Program Mathematical Economics

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

    Updated on Jul 20, 2021 10:09 AM PDT
  107. Program Computational Complexity

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

    Updated on Mar 08, 2022 10:14 AM PST
  108. Program Differential Geometry

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

    Updated on Dec 04, 2021 07:05 AM PST
  109. Program Low-dimensional Topology

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

    Updated on Apr 22, 2022 01:09 PM PDT
  110. Program Infinite-Dimensional Lie Algebras

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

    Updated on Jun 05, 2019 02:31 PM PDT
  111. Program Ergodic Theory and Dynamical Systems

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

    Updated on May 06, 2022 03:27 PM PDT
  112. Program Mathematical Statistics

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

    Updated on May 19, 2021 02:22 PM PDT