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Scientific Programs

Acknowledged as the premier center for collaborative mathematical research, MSRI organizes and hosts semester-length (or year-long) 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.

MSRI invites the submission of proposals for full-year or half-year programs to be held at MSRI. Planning such programs is generally done about three years in advance. Except in extraordinary cases, a subject is the focus of a program not more than once in ten years.


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Current Programs

  1. 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 (University of Texas, Austin), Anna Wienhard (Ruprecht-Karls-Universität Heidelberg), Anton Zorich (Institut de Mathematiques de Jussieu)
    Quadmesh2
    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 Aug 30, 2019 11:48 AM PDT
  2. 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 de Paris XI (Paris-Sud)), 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
  3. 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

Upcoming Programs

  1. 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 (University of Illinois at Urbana-Champaign)
    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 Mar 22, 2018 11:21 AM PDT
  2. 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 Oct 05, 2018 12:21 PM PDT
  3. Random and Arithmetic Structures in Topology

    Organizers: Nicolas Bergeron (Université de Paris VI (Pierre et Marie Curie)), Jeffrey Brock (Brown 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

    The use of dynamical invariants has long been a staple of geometry and topology, from rigidity theorems, to classification theorems, to the general study of lattices and of the mapping class group. More recently, random structures in topology and notions of probabilistic geometric convergence have played a critical role in testing the robustness of conjectures in the arithmetic setting. The program will focus on invariants in topology, geometry, and the dynamics of group actions linked to random constructions.

    Updated on Apr 22, 2019 01:56 PM PDT
  4. Decidability, definability and computability in number theory

    Organizers: 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), LEAD Thomas Scanlon (University of California, Berkeley), Alexandra Shlapentokh (East Carolina University), Carlos Videla (Mount Royal University)

    This program is focused on the two-way interaction of logical ideas and techniques, such as definability from model theory and decidability from computability theory, with fundamental problems in number theory. These include analogues of Hilbert's tenth problem, isolating properties of fields of algebraic numbers which relate to undecidability, decision problems around linear recurrence and algebraic differential equations, the relation of transcendence results and conjectures to decidability and decision problems, and some problems in anabelian geometry and field arithmetic. We are interested in this specific interface across a range of problems and so intend to build a semester which is both more topically focused and more mathematically broad than a typical MSRI program.

    Updated on May 10, 2019 03:25 PM PDT
  5. Mathematical problems in fluid dynamics

    Organizers: Thomas Alazard (École Normale Supérieure; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Université Paris-Est Créteil Val-de-Marne; Centre National de la Recherche Scientifique (CNRS)), Mihaela Ifrim (University of Wisconsin-Madison), Igor Kukavica (University of Southern California), David Lannes (Université de Bordeaux I; Centre National de la Recherche Scientifique (CNRS)), LEAD Daniel Tataru (University of California, Berkeley)
    Barcuta

    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 Apr 25, 2019 02:32 PM PDT
  6. 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 Washington), Alice Guionnet (École Normale Supérieure de Lyon), Alexander Its (Indiana University-Purdue University Indianapolis), Herbert Spohn (Technische Universität München), Horng-Tzer Yau (Harvard University)
    Image

    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 Apr 24, 2019 03:08 PM PDT
  7. The Analysis and Geometry of Random Spaces

    Organizers: LEAD Mario Bonk (University of California, Los Angeles), Joan Lind (University of Tennessee), Steffen Rohde (University of Washington), Eero Saksman (University of Helsinki), Fredrik Viklund (Royal Institute of Technology), Jang-Mei Wu (University of Illinois at Urbana-Champaign)
    Graphisc

    This program is devoted to the investigation of universal analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics. Prominent examples for recent developments are the Schramm-Loewner evolution, the continuum random tree, Bernoulli percolation on the integers,  random surfaces produced by Liouville Quantum Gravity, and Jordan curves and dendrites obtained from random conformal weldings and laminations. The lack of regularity of these random structures often results in a failure of classical methods of analysis. One goal of this program is to enrich the analytic toolbox to better handle these rough structures.

    Updated on Jul 12, 2019 05:49 PM PDT
  8. Complex Dynamics: from special families to natural generalizations in one and several variables

    Organizers: LEAD Sarah Koch (University of Michigan), Jasmin Raissy (Institut de Mathématiques de Toulouse), Dierk Schleicher (Jacobs University Bremen), Mitsuhiro Shishikura (Kyoto University), Dylan Thurston (Indiana University)
    Image
    The mating of these two dendritic Julia sets is equal to the Julia set of a rational map of degree 2; that Julia set is equal to the entire Riemann sphere.

    Holomorphic dynamics is a vibrant field of mathematics that has seen profound progress over the past 40 years. It has numerous interconnections to other fields of mathematics and beyond. 

    Our semester will focus on three selected classes of dynamical systems: rational maps (postcritically finite and beyond); transcendental maps; and maps in several complex variables. We will put particular emphasis on the interactions between each these, and on connections with adjacent areas of mathematics. 

    Updated on Apr 15, 2019 10:38 AM PDT

Past Programs

  1. 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
  2. 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)
    Image
    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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. Program 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-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 Apr 21, 2015 03:40 PM PDT
  17. 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
  18. 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
  19. 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
  20. Program Dynamics on Moduli Spaces of Geometric Structures

    Organizers: Richard Canary (University of Michigan), William Goldman (University of Maryland), François Labourie (Université Côte d'Azur), 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
  21. 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 Aug 13, 2014 09:08 AM PDT
  22. 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
  23. 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
  24. Program Algebraic Topology

    Organizers: Vigleik Angeltveit (Australian National University), Andrew Blumberg (University of Texas, Austin), 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 May 01, 2019 02:00 PM PDT
  25. Program Mathematical General Relativity

    Organizers: Yvonne Choquet-Bruhat, Piotr Chrusciel (Universität Wien), Greg Galloway (University of Miami), Gerhard Huisken (Math. Forschungsinstitut Oberwolfach), LEAD James Isenberg (University of Oregon), Sergiu Klainerman (Princeton University), Igor Rodnianski (Massachusetts Institute of Technology), Richard Schoen (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
  26. 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 May 01, 2019 01:23 PM PDT
There are more then 30 past programs. Please go to Past programs to see all past programs.