Acknowledged as the premier center for collaborative mathematical research, MSRI organizes and hosts semesterlength (or yearlong) 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 fullyear or halfyear 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.
Additional Resources
 Membership applications and deadlines
 Programrelated workshops (conferences) held at MSRI
 Submitting a proposal for a future Program
Current Programs

Mathematics and Computer Science of Market and Mechanism Design
Organizers: Martin Bichler (Technical University of Munich), Péter Biró (KRTK, Eotvos Lorand Research Network), Michal Feldman (TelAviv University), Nicole Immorlica (Microsoft Research), LEAD Scott Kominers (Harvard Business School), Shengwu Li (Harvard University), Paul Milgrom (Stanford University), Alvin Roth (Stanford University), Eva Tardos (Cornell University)In recent years, economists and computer scientists have collaborated with mathematicians, operations research experts, and practitioners to improve the design and operations of realworld marketplaces. Such work relies on robust feedback between theory and practice, inspiring new mathematics closely linked – and directly applicable – to market and mechanism design questions. This crossdisciplinary program seeks to expand the domains in which existing market design solutions can be applied; address foundational questions regarding our ways of developing and evaluating mechanisms; and build useful analytic frameworks for applying theory to practical marketplace design.
Updated on Sep 05, 2023 11:05 AM PDT 
Algorithms, Fairness, and Equity
Organizers: Vincent Conitzer (Carnegie Mellon University), Moon Duchin (Tufts University), Bettina Klaus (University of Lausanne), Jonathan Mattingly (Duke University), LEAD Wesley Pegden (Carnegie Mellon University)This program aims to bring together researchers working at the interface of fairness and computation. This interface has been the site of intensive research effort in mechanism design, in research on partitioning problems related to political districting problems, and in research on ways to address issues of fairness and equity in the context of machine learning algorithms.
These areas each approach the relationship between mathematics and fairness from a distinct perspective. In mechanism design, algorithms are a tool to achieve outcomes with mathematical guarantees of various notions of fairness. In machine learning, we perceive failures of fairness as an undesirable side effect of learning approaches, and seek mathematical approaches to understand and mitigate these failures. And in partitioning problems like political districting, we often seek mathematical tools to evaluate the fairness of human decisions.
This program will explore progress in these areas while also providing a venue for overlapping perspectives. The topics workshop “Randomization, neutrality, and fairness” will explore the common role randomness and probability has played in these lines of work.
Updated on Aug 24, 2023 07:26 AM PDT 
Complementary Program 202324
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 Sep 26, 2023 11:36 AM PDT
Upcoming Programs

Commutative Algebra
Organizers: Aldo Conca (Università di Genova), Steven Cutkosky (University of Missouri), LEAD Claudia Polini (University of Notre Dame), Claudiu Raicu (University of Notre Dame), Steven Sam (University of California, San Diego), Kevin Tucker (University of Illinois at Chicago), Claire Voisin (Collège de France; Institut de Mathématiques de Jussieu)Commutative algebra is, in its essence, the study of algebraic objects, such as rings and modules over them, arising from polynomials and integral numbers. It has numerous connections to other fields of mathematics including algebraic geometry, algebraic number theory, algebraic topology and algebraic combinatorics. Commutative Algebra has witnessed a number of spectacular developments in recent years, including the resolution of longstanding problems, with new techniques and perspectives leading to an extraordinary transformation in the field. The main focus of the program will be on these developments. These include the recent solution of Hochster's direct summand conjecture in mixed characteristic that employs the theory of perfectoid spaces, a new approach to the BuchsbaumEisenbudHorrocks conjecture on the Betti numbers of modules of finite length, recent progress on the study of CastelnuovoMumford regularity, the proof of Stillman's conjecture and ongoing work on its effectiveness, a novel strategy to Green's conjecture on the syzygies of canonical curves based on the study of Koszul modules and their generalizations, new developments in the study of various types of multiplicities, theoretical and computational aspects of Gröbner bases, and the implicitization problem for Rees algebras and its applications.
Updated on May 24, 2022 10:29 AM PDT 
Noncommutative Algebraic Geometry
Organizers: Wendy Lowen (Universiteit Antwerpen), Alex Perry (University of Michigan), LEAD Alexander Polishchuk (University of Oregon), Susan Sierra (University of Edinburgh), Spela Spenko (Université Libre de Bruxelles), Michel Van den Bergh (Hasselt University)Derived categories of coherent sheaves on algebraic varieties were originally conceived as technical tools for studying cohomology, but have since become central objects in fields ranging from algebraic geometry to mathematical physics, symplectic geometry, and representation theory. Noncommutative algebraic geometry is based on the idea that any category sufficiently similar to the derived category of a variety should be regarded as (the derived category of) a “noncommutative algebraic variety”; examples include semiorthogonal components of derived categories, categories of matrix factorizations, and derived categories of noncommutative dgalgebras. This perspective has led to progress on old problems, as well as surprising connections between seemingly unrelated areas. In recent years there have been great advances in this domain, including new tools for constructing semiorthogonal decompositions and derived equivalences, progress on conjectures relating birational geometry and singularities to derived categories, constructions of moduli spaces from noncommutative varieties, and instances of homological mirror symmetry for noncommutative varieties. The goal of this program is to explore and expand upon these developments.
Updated on May 19, 2022 01:51 PM PDT 
Quantum Symmetries Reunion
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 Galoislike 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 Sep 14, 2023 04:03 AM PDT 
New Frontiers in Curvature: Flows, General Relativity, Minimal Submanifolds, and Symmetry
Organizers: LEAD Ailana Fraser (University of British Columbia), LanHsuan Huang (University of Connecticut), Richard Schoen (University of California, Irvine), LEAD Catherine Searle (Wichita State University), Lu Wang (Yale University), Guofang Wei (University of California, Santa Barbara)Geometry, PDE, and Relativity are subjects that have shown intriguing interactions in the past several decades, while simultaneously diverging, each with an ever growing number of branches. Recently, several major breakthroughs have been made in each of these fields using techniques and ideas from the others.
This program is aimed at connecting various branches of Geometry, PDE, and Relativity and at enhancing collaborations across these disciplines and will include four main topics: Geometric Flows, Geometric problems in Mathematical Relativity, Global Riemannian Geometry, and Minimal Submanifolds. Specifically the program focuses on a central goal, which is to advance our knowledge toward Riemannian (sub)manifolds under geometric conditions, such as curvature lower bounds, by developing techniques in, for example, geometric flows and minimal submanifolds and further fostering new connections.
Updated on Nov 17, 2022 10:10 AM PST 
Special Geometric Structures and Analysis
Organizers: Eleonora Di Nezza (Institut de Mathématiques de Jussieu), LEAD Mark Haskins (Duke University), Tristan Riviere (ETH Zurich), Song Sun (University of California, Berkeley), Xuwen Zhu (Northeastern University)This program sits at the intersection between differential geometry and analysis but also connects to several other adjacent mathematical fields and to theoretical physics. Differential geometry aims to answer questions about very regular geometric objects (smooth Riemannian manifolds) using the tools of differential calculus. A fundamental object is the curvature tensor of a Riemannian metric: an algebraically complicated object that involves 2nd partial derivatives of the metric. Many questions in differential geometry can therefore be translated into questions about the existence or properties of the solutions of systems of (often) nonlinear partial differential equations (PDEs). The PDE systems that arise in geometry have historically stimulated the development of powerful new analytic methods. In most cases the nonlinearity of these systems makes ‘closed form’ expressions for a solution impossible: instead more abstract methods must be employed.
Updated on Nov 10, 2022 04:20 PM PST 
Probability and Statistics of Discrete Structures
Organizers: Louigi AddarioBerry (McGill University), Christina Goldschmidt (University of Oxford), PoLing Loh (University of Cambridge), Gabor Lugosi (Barcelona School of Economics), Dana Randall (Georgia Institute of Technology), LEAD Remco van der Hofstad (Technische Universiteit Eindhoven)Random graphs and related random discrete structures lie at the forefront of applied probability and statistics, and are core topics across a wide range of scientific disciplines where mathematical ideas are used to model and understand realworld networks. At the same time, random graphs pose challenging mathematical and algorithmic problems that have attracted attention from probabilists and combinatorialists since at least 1960, following the pioneering work of Erdős and Renyi.
Around the turn of the millennium, as very large data sets became available, several applied disciplines started to realize that many realworld networks, even though they are from various origins, share fascinating features. In particular, many such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scalefree, in the sense that the number of connections made by their elements is extremely heterogeneous. This program is devoted to the study of the probabilistic and statistical properties of such networks. Central tools include graphon theory for dense graphs, local weak convergence for sparse graphs, and scaling limits for the critical behavior of graphs or stochastic processes on them. The program is aimed at pure and applied mathematicians interested in network problems.Updated on Sep 14, 2023 10:08 AM PDT 
Extremal Combinatorics
Organizers: LEAD David Conlon (California Institute of Technology), LEAD Jacob Fox (Stanford University), Penny Haxell (University of Waterloo), Janos Pach (Alfréd Rényi Institute of Mathematics), Maya Stein (Universidad de Chile), Andrew Suk (University of California, San Diego)Extremal combinatorics concerns itself with problems about how large or small a finite collection of objects can be while satisfying certain conditions. Questions of this type arise naturally across mathematics, so this area has close connections and interactions with a broad array of other fields, including number theory, group theory, model theory, probability, statistical physics, optimization, and theoretical computer science.
The area has seen huge growth in the twentyfirst century and, particularly in recent years, there has been a steady stream of solutions to important longstanding problems and many powerful new methods have been introduced. These advances include improvements in absorption techniques which have facilitated the proof of the existence of designs and related objects, the breakthrough on the sunflower conjecture whose further development eventually led to the proof of the Kahn–Kalai conjecture in discrete probability and the discovery of interactions between spectral graph theory and the study of equiangular lines in discrete geometry. These and other groundbreaking advances will be the central theme of the semester program on “Extremal Combinatorics” at SLMath.
In this program, we will bring together experts as well as enthusiastic young researchers to learn from each other, to initiate and continue collaborations, to communicate recent work, and to further advance the field by making progress on fundamental open problems and developing further connections with other branches of mathematics. We trust that younger mathematicians will greatly contribute to the success of the program with their new ideas. It is our hope that this program will provide a unique opportunity for women and underrepresented groups to make outstanding contributions to the field and we strongly encourage their participation.
Updated on Feb 27, 2023 03:02 PM PST 
Kinetic theory: Novel statistical, stochastic and analytical methods
Organizers: Laurent Desvillettes (Université de Paris VII (Denis Diderot)), Irene M. Gamba (University of Texas, Austin), Francois Golze (École Polytechnique), LEAD Pierre Emmanuel Jabin (Pennsylvania State University), Qin Li (University of WisconsinMadison), Chiara Saffirio (Universität Basel), Lexing Ying (Stanford University)The focus of the proposed program is on socalled kinetic equations, describing the evolution of the of manyparticle interacting systems. These models have the form of statistical flows, with their solutions being either a single or multiple point probability density functions or measures, supported in a space of attributes. The attributes are problemdependent and can be molecular velocity, energy, opinion, wealth, and many others. The flow then predicts the evolution of the probability measure in time, position in space, and the interchanging of the particles' states by the transition probability.
Probably the most classical kinetic equation is the Boltzmann equation which describes the evolutions of the phasespace density function for a dilute gas under binary molecular collisions. Other wellknown classical kinetic models include the Landau equation, Vlasov equation for plasmas or other systems, FokkerPlanck equations or kinetic formulations of various macroscopic or hyperbolic systems.
In recent years, the successes of kinetic theory gave rise to an rapidly increasing variety of mathematical models beyond physics to applications in life sciences, social sciences, economy. Even more recently fascinating connections between kinetic theory and some aspects of data science have emerged.
Kinetic theory has strong and fascinating interactions with a large variety of other fields, including statistical mechanics, stochastic processes, dynamical systems...
The program will strive to give an overview of the novel mathematical tools used in kinetic theory through a broad range of classical and more recent applications.
Updated on Sep 18, 2023 02:50 PM PDT 
Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups
Organizers: Martin Bridgeman (Boston College), Richard Canary (University of Michigan), Amir Mohammadi (University of California, San Diego), Hee Oh (Yale University), Maria Beatrice Pozzetti (RuprechtKarlsUniversität Heidelberg), JeanFrançois Quint (Université de Bordeaux I)This research program will bring together two intellectual communities that have made significant advances in the study of discrete subgroups of higher rank semisimple Lie groups: the homogeneous dynamics community and the community studying geometric structures and Anosov groups.
A discrete subgroup Γ of a semisimple Lie group G may be studied from many different viewpoints. On the one hand, the quotient G/Γ is a homogenous space; through the lens of homogeneous dynamics one can study flows on these spaces, their orbit closures, measure classifications, counting and equidistributions. On the other hand, the group G acts on a plethora of different geometries, including Riemannian and nonRiemannian symmetric spaces, projective spaces and flag manifolds. In many cases, this induces interesting properly discontinuous actions of Γ which can be studied using geometric methods. A flexible class of such discrete subgroups is given by Anosov groups, introduced by Labourie in his study of Hitchin representations and now accepted as the natural higher rank analogue of convex cocompact subgroups of rank one Lie groups. In recent years, their study has made tremendous advances by drawing inspiration from classical Teichmuller theory, and the theory of Kleinian groups.
When G has rank one, there has already been a fruitful interaction between the two communities, resulting in important advances in understanding the dynamics of the frame flow and unipotent flow on the frame bundle of convex cocompact and geometrically finite hyperbolic manifolds. In turn this had important applications to Apollonian circle packings, Zaremba’s conjecture, expanders, affine sieve problems for thin groups, and related problems, as well as groundberaking work in Teichmuller dynamics.
Exciting applications of the interaction between homogeneous dynamics and Anosov representations have begun to emerge in recent years, suggesting that now is very promising time to bring together these two communities. The notion of a thin subgroup, inspired from number theory, is one of the many points of convergence. Other recent advances include the study of homogeneous
dynamics in the setting of Borel Anosov groups, relations between the Hausdorff dimension of limit sets of Anosov groups with counting problems, as well as applications of the thermodynamical formalism in the study of Anosov representations. A strong link between Anosov groups and Hilbert geometry recently opened the door to a very active study of dynamics in these geometries.
This recent work seems likely to be just the first fruit of the interaction between dynamics and geometry for discrete subgroups of semisimple Lie groups.Updated on Sep 19, 2023 12:59 PM PDT 
Topological and Geometric Structures in Low Dimensions
Organizers: Ian Agol (University of California, Berkeley), Kenneth Bromberg (University of Utah), Sebastian Hensel (LMU München), Christopher Leininger (Rice University), Kathryn Mann (Cornell University), LEAD Yair Minsky (Yale University), Rachel Roberts (Washington University)Low dimensional topology is a meeting place for ideas, objects and techniques that interact richly with each other, and generate implications for many parts of mathematics. Geometric structures, such as hyperbolic structures on 2 and 3manifolds, interact with dynamical properties of flows and with analysis on parameter spaces such as the Teichmuller space of a surface or a foliation by surfaces. Combinatorial objects such as complexes of curves and their generalizations give us insight into the behavior of mapping class groups, which encapsulate the topological symmetries of a surface, as well as homeomorphism and diffeomorphism groups which blend topology and dynamics.
Seminal work of Thurston in the 1970’s brought many of these ideas together in new ways, and inspired multiple lines of work in the time since then, exploring different aspects of the relationship between geometry, topology, analysis and dynamics. Recent progress in these fields has taken each in new directions, suggesting that refocusing on their interactions will yield dividends towards progress on key problems within this central area and grow outwards towards its many connections with other areas of mathematics.
As examples of structural questions in the overlap of these areas: How do we classify Anosov and pseudoAnosov flows on 3manifolds up to orbit equivalence? Can we relate the dynamics of pseudoAnosov flows on hyperbolic 3manifolds to the geometry of the underlying 3manifolds? Can we relate the leafwise Teichmuller theory of a foliation to geometric structures on the underlying 3manifold? How well can we understand the subgroup structure of homeomorphism and diffeomorphism groups of surfaces? Can mapping class groups of infinitetype surfaces be harnessed to study dynamical questions?
The program will bring together experts in all these fields and younger researchers, who together can address these sorts of questions and open new areas for exploration.
Updated on Sep 19, 2023 12:49 PM PDT
Past Programs

Program Complementary Program 202223
Updated on Aug 07, 2023 05:47 PM PDT 
Program Mathematical Problems in Fluid Dynamics, part 2
Organizers: Thomas Alazard (Ecole Normale Supérieure ParisSaclay; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Laboratoire JacquesLouis Lions; Centre National de la Recherche Scientifique (CNRS)), Mihaela Ifrim (University of WisconsinMadison), Igor Kukavica (University of Southern California), David Lannes (Institut de Mathématiques de Bordeaux; Centre National de la Recherche Scientifique (CNRS)), Daniel Tataru (University of California, Berkeley)PROGRAM DESCRIPTION
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 wellknown Euler equations for inviscid fluids, and the NavierStokes 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 18, 2023 04:16 PM PDT 
Program Simons Bridge Postdoctoral Fellowship 2022/23
Updated on Feb 10, 2022 10:34 AM PST 
Program Algebraic Cycles, LValues, and Euler Systems
Organizers: Henri Darmon (McGill University), Ellen Eischen (University of Oregon), LEAD Benjamin Howard (Boston College), David Loeffler (University of Warwick), Christopher Skinner (Princeton University), Sarah Zerbes (ETH Zürich), Wei Zhang (Massachusetts Institute of Technology)The fundamental conjecture of Birch and SwinnertonDyer relating the Mordell–Weil ranks of elliptic curves to their Lfunctions is one of the most important and motivating problems in number theory. It resides at the heart of a collection of important conjectures (due especially to Deligne, Beilinson, Bloch and Kato) that connect values of Lfunctions and their leading terms to cycles and Galois cohomology groups.
The study of special algebraic cycles on Shimura varieties has led to progress in our understanding of these conjectures. The arithmetic intersection numbers and the padic regulators of special cycles are directly related to the values and derivatives of Lfunctions, as shown in the pioneering theorem of GrossZagier and its padic avatars for Heegner points on modular curves. The cohomology classes of special cycles (and related constructions such as Eisenstein classes) form the foundation of the theory of Euler systems, providing one of the most powerful methods known to prove vanishing or finiteness results for Selmer groups of Galois representations.
The goal of this semester is to bring together researchers working on different aspects of this young but fastdeveloping subject, and to make progress on understanding the mysterious relations between Lfunctions, Euler systems, and algebraic cycles.
Updated on Jan 11, 2023 12:03 PM PST 
Program Diophantine Geometry
Organizers: Jennifer Balakrishnan (Boston University), Mirela Ciperiani (University of Texas, Austin), Philipp Habegger (University of Basel), Wei Ho (Institute for Advanced Study), LEAD Hector Pasten (Pontificia Universidad Católica de Chile), Yunqing Tang (University of California, Berkeley), ShouWu Zhang (Princeton University)While the study of rational solutions of diophantine equations initiated thousands of years ago, our knowledge on this subject has dramatically improved in recent years. Especially, we have witnessed spectacular progress in aspects such as height formulas and height bounds for algebraic points, automorphic methods, unlikely intersection problems, and nonabelian and padic approaches to algebraic degeneracy of rational points. All these groundbreaking advances in the study of rational and algebraic points in varieties will be the central theme of the semester program “Diophantine Geometry” at MSRI. The main purpose of this program is to bring together experts as well as enthusiastic young researchers to learn from each other, to initiate and continue collaborations, to update on recent breakthroughs, and to further advance the field by making progress on fundamental open problems and by developing further connections with other branches of mathematics. We trust that younger mathematicians will greatly contribute to the success of the program with their new ideas. It is our hope that this program will provide a unique opportunity for women and underrepresented groups to make outstanding contributions to the field, and we strongly encourage their participation.
Updated on Jan 11, 2023 03:21 PM PST 
Program Floer Homotopy Theory
Organizers: Mohammed Abouzaid (Columbia University), Andrew Blumberg (Columbia University), Kristen Hendricks (Rutgers University), Robert Lipshitz (University of Oregon), LEAD Ciprian Manolescu (Stanford University), Nathalie Wahl (University of Copenhagen)The development of Floer theory in its early years can be seen as a parallel to the emergence of algebraic topology in the first half of the 20th century, going from counting invariants to homology groups, and beyond that to the construction of algebraic structures on these homology groups and their underlying chain complexes. In continuing work that started in the latter part of the 20th century, algebraic topologists and homotopy theorists have developed deep methods for refining these constructions, motivated in large part by the application of understanding the classification of manifolds. The goal of this program is to relate these developments to Floer theory with the dual aims of (i) making progress in understanding symplectic and lowdimensional topology, and (ii) providing a new set of geometrically motivated questions in homotopy theory.
Updated on Aug 19, 2022 12:45 PM PDT 
Program Analytic and Geometric Aspects of Gauge Theory
Organizers: Laura Fredrickson (University of Oregon), Rafe Mazzeo (Stanford University), Tomasz Mrowka (Massachusetts Institute of Technology), Laura Schaposnik (University of Illinois at Chicago), LEAD Thomas Walpuski (HumboldtUniversität)The mathematics and physics around gauge theory have, since their first interaction in the mid 1970’s, prompted tremendous developments in both mathematics and physics. Deep and fundamental tools in partial differential equations have been developed to provide rigorous foundations for the mathematical study of gauge theories. This led to ongoing revolutions in the understanding of manifolds of dimensions 3 and 4 and presaged the development of symplectic topology. Ideas from quantum field theory have provided deep insights into new directions and conjectures on the structure of gauge theories and suggested many potential applications. The focus of this program will be those parts of gauge theory which hold promise for new applications to geometry and topology and require development of new analytic tools for their study.
Updated on Aug 25, 2022 01:29 PM PDT 
Program Definability, Decidability, and Computability in Number Theory, part 2
Organizers: Valentina Harizanov (George Washington University), Barry Mazur (Harvard University), Russell Miller (Queens College, CUNY; CUNY, Graduate Center), Jonathan Pila (University of Oxford), Thomas Scanlon (University of California, Berkeley), Alexandra Shlapentokh (East Carolina University)This program is focused on the twoway 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 Dec 21, 2021 09:51 AM PST 
Program Complementary Program 202122
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 May 03, 2022 02:54 PM PDT 
Program Simons Bridge Postdoctoral Fellowship 2021/22
Updated on Feb 10, 2022 10:34 AM PST 
Program Higher Categories and Categorification, Part Two
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 (MaxPlanckInstitut für Mathematik), Dominic Verity (Macquarie University)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 localtoglobal 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_nalgebras suggests. Higher categories offer unforeseen characterizing universal properties for familiar constructions such as Ktheory. 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 Jun 06, 2022 12:39 PM PDT 
Program 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), JangMei Wu (University of Illinois at UrbanaChampaign)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 SchrammLoewner 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 Dec 21, 2021 12:37 PM PST 
Program 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 Bordeaux), Dierk Schleicher (Université d'AixMarseille (AMU)), Mitsuhiro Shishikura (Kyoto University), Dylan Thurston (Indiana University)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 Jan 20, 2022 09:31 AM PST 
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 UniversityPurdue University), Herbert Spohn (Technische Universität München), HorngTzer 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 
Program Complementary Program 202021
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 
Program Mathematical problems in fluid dynamics
Organizers: Thomas Alazard (Ecole Normale Supérieure ParisSaclay; Centre National de la Recherche Scientifique (CNRS)), Hajer Bahouri (Laboratoire JacquesLouis Lions; Centre National de la Recherche Scientifique (CNRS)), Mihaela Ifrim (University of WisconsinMadison), 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.
PROGRAM DESCRIPTION
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 wellknown Euler equations for inviscid fluids, and the NavierStokes 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 Oct 05, 2022 11:30 AM PDT 
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 FriedrichWilhelmsUniversität Bonn), Fanny Kassel (Institut des Hautes Études Scientifiques (IHES)), LEAD Alan Reid (Rice University)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 
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)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 
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)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 Galoislike 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 
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 (MaxPlanckInstitut für Mathematik), Dominic Verity (Macquarie University)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 localtoglobal 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_nalgebras suggests. Higher categories offer unforeseen characterizing universal properties for familiar constructions such as Ktheory. 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 
Program Complementary Program 201920
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 
Program Holomorphic Differentials in Mathematics and Physics
Organizers: LEAD Jayadev Athreya (University of Washington), Steven Bradlow (University of Illinois at UrbanaChampaign), Sergei Gukov (California Institute of Technology), Andrew Neitzke (Yale University), Anna Wienhard (Max Planck Institute for Mathematics in the Sciences), Anton Zorich (Institut de Mathematiques de Jussieu)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 Fukayatype categories, links to quantum integrable systems, or the physically derived construction of socalled 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 lowdimensional 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 
Program Microlocal Analysis
Organizers: Pierre Albin (University of Illinois at UrbanaChampaign), Nalini Anantharaman (Université de Strasbourg), Kiril Datchev (Purdue University), Raluca Felea (Rochester Institute of Technology), Colin Guillarmou (Université ParisSaclay), LEAD Andras Vasy (Stanford University)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 
Program 2019 African Diaspora Joint Mathematics Workshop (ADJOINT) program
Updated on Mar 21, 2019 01:22 PM PDT 
Program Complementary Program 201819
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 
Program Derived Algebraic Geometry
Organizers: Julie Bergner (University of Virginia), LEAD Bhargav Bhatt (Institute for Advanced Study), Dennis Gaitsgory (Harvard University), David Nadler (University of California, Berkeley), Nick Rozenblyum (University of Chicago), Peter Scholze (Universität Bonn), Gabriele Vezzosi (Università di Firenze)Derived algebraic geometry is an extension of algebraic geometry that provides a convenient framework for directly treating nongeneric geometric situations (such as nontransverse 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 
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 CalabiYau Varieties in Geometry, Arithmetic and the Physics of String TheoryUpdated on Jan 31, 2017 07:46 PM PST 
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 
Program Summer Research for Women in Mathematics
Organizers: Hélène Barcelo (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath))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 
Program Complementary Program 201718
Updated on Nov 30, 2017 03:30 PM PST