Logo

Mathematical Sciences Research Institute

Home > Education > For Graduate Students

For Graduate Students

Our Summer Graduate Schools have been designed for graduate students at different levels. Each school typically has a track for beginning students and a track for more advanced students.

In addition the connections for women and introductory workshops that accompany each program our often appropriate for graduate students. Of course advanced graduate students may also benefit from scientific workshops at the institute when the topic matches their research interest. Students should periodically check the list of upcoming workshops to see when something appropriate is available.

Faculty visiting the institute for an extended period of time may sometimes bring graduate students who will stay as program associates.
No current Summer Graduate Schools
  1. Seminaire de Mathematiques Superieures 2015: Geometric and Computational Spectral Theory

    Organizers: Alexandre Girouard (Laval University), Dmitry Jakobson (McGill University), Michael Levitin (University of Reading), Nilima Nigam (Simon Fraser University), Iosif Polterovich (Université de Montréal), Frederic Rochon (Université du Québec à Montréal)

    The lectures will focus on the following four topics: geometry of eigenvalues, geometry of eigenfunctions, spectral theory on manifolds with singularities and computational spectral theory. There has been a number of remarkable recent developments in these closely related fields. The goal of the school is to shed light on different facets of modern spectral theory and to provide a unique opportunity for graduate students and young researchers to get a “big picture” of this rapidly evolving area of mathematics. A particularly novel aspect of the school is the emphasis on the interactions between spectral geometry and computational spectral theory.

    Updated on Sep 03, 2014 01:11 PM PDT
  2. Geometric Group Theory

    Organizers: LEAD John Mackay (University of Bristol), Anne Thomas (University of Glasgow), Kevin Wortman (University of Utah)

    The aim of this workshop is to introduce graduate students to some specific core topics which will be under study at the upcoming MSRI program on Geometric Group Theory (GGT) in 2016.  GGT encompasses a wide range of topics. The four minicourse topics have been chosen because they are central themes in GGT and in the upcoming MSRI program. Moreover, each topic is accessible to students with a range of backgrounds: the basic definitions are straightforward, with many simple and illuminating examples to work through, yet lead through to important questions in current research.

    Updated on Aug 28, 2014 01:51 PM PDT
  3. CRM-PIMS Summer School in Probability

    Organizers: LEAD Louigi Addario-Berry (McGill University), Omer Angel, Louis-Pierre Arguin, Martin Barlow, Edwin Perkins, Lea Popovic (Concordia University)

    The 2015 CRM-PIMS Summer School in Probability will take place in Montreal, Canada, from June 15-July 11, 2015. The school is built around two principal 24-hour lecture courses, which will be delivered by Alice Guionnet (random matrices, free probability and the enumeration of maps) and Remco van der Hofstad (high-dimensional percolation and random graphs). There will additionally be mini-courses by Louigi Addario-Berry (random minimum spanning trees), Shankar Bhamidi (dynamic random network models) and Jonathan Mattingly (stabilization by noise). Some time is reserved for participants to present their own work.

    Updated on Nov 03, 2014 09:28 AM PST
  4. Mathematical Topics in Systems Biology

    Organizers: LEAD Steven Altschuler (University of California, San Francisco), Lani Wu (University of California, San Francisco)

    This Summer Graduate School will introduce mathematics graduate students to the rapidly emerging area of systems biology. In particular, we will focus on the design and emergent behaviors of molecular networks used by cells to interpret their environments and create robust temporal-spatial behaviors. This will be a very hands-on workshop with students working alone and in teams to program and present key ideas.

    Updated on Aug 28, 2014 12:08 PM PDT
  5. NIMS Summer School on Random Matrix Theory

    Organizers: LEAD Jinho Baik (University of Michigan)

    This summer graduate school will take place at the National Institute for Mathematical Sciences in Daejeon, South Korea.  The purpose of this summer school is to introduce some of the basic ideas and methods of random matrix theory to graduate students.  In particular there will be three lecture series on random matrix theory from three different perspectives: from the view points of the integrable structures, the moment method, and the Stieltjes transorm technique.  In addition to the lectures, there will be discussion sessions, and the students will also have plenty of time to interact with the lecturers and with other students.

    Please note that accepted students will be provided up to $1700 in travel reimbursement, in addition to meals and accommodation.

    Updated on Nov 20, 2014 12:02 PM PST
  6. Gaps between Primes and Analytic Number Theory

    Organizers: Andrew Granville (Université de Montréal), LEAD Emmanuel Kowalski (Eidgenössische TH Zürich-Hönggerberg), James Maynard (University of Oxford), Kannan Soundararajan (Stanford University)

    These courses will give students a full overview of the results of Zhang and Maynard on gaps between primes, and will provide them will a clear understanding of the tools involved. This will make accessible a significant part of modern analytic number theory. The lecturers will also make sure to include, within their course, examples and discussions going further than is strictly required to understand the proofs of Zhang and Maynard, e.g., in the direction of automorphic forms and the Riemann Hypothesis over finite fields.

    Updated on Oct 13, 2014 11:27 AM PDT
  7. Incompressible Fluid Flows at High Reynolds Number

    Organizers: Jacob Bedrossian (University of Maryland), LEAD Vlad Vicol (Princeton University)

    The purpose of this two week workshop is to introduce graduate students to state-of-the-art methods and results in mathematical fluid dynamics. In the first week, we will discuss the mathematical foundations and modern analysis aspects of the Navier-Stokes and Euler equations. In the second week, we will run two courses concurrently on the topics of inviscid limits and hydrodynamic stability. Specifically, one course will focus on boundary layers in high Reynolds number flows and the Prandtl equations while the other will focus on mixing and connections to turbulence. Through the lectures and associated problem sessions, the students will learn about a number of new analysis tools and principles of fluid mechanics that are not always taught in a graduate school curriculum.

    Updated on Aug 28, 2014 08:47 AM PDT

Past SummerSchools

  1. Geometry and Analysis

    Organizers: Hans-Joachim Hein (Imperial College, London), LEAD Aaron Naber (Massachusetts Institute of Technology)

    Geometric and complex analysis is the application of tools from analysis to study questions from geometry and topology. This two week summer course will provide graduate students with the necessary background to begin studies in the area. The first week will consist of introductory courses on geometric analysis, complex analysis, and Riemann surfaces. The second week will consist of more advanced courses on the regularity theory of Einstein manifolds, Kahler-Einstein manifolds, and the analysis of Riemann surfaces.

    Updated on Aug 11, 2014 12:16 PM PDT
  2. Stochastic Partial Differential Equations

    Organizers: Yuri Bakhtin (New York University, Courant Institute), LEAD Ivan Corwin (Columbia University), James Nolen (Duke University)

    Stochastic Partial Differential Equations (SPDEs) serve as fundamental models of physical systems subject to random inputs, interactions or environments. It is a particular challenge to develop tools to construct solutions, prove robustness of approximation schemes, and study properties like ergodicity and fluctuation statistics for a wide variety of SPDEs. 

    The purpose of this two week workshop is to educate graduate students on the state-of-the-art methods and results in SPDEs. The three courses which will be run simultaneously will highlight different (though related) aspects of this area including (1) Fluctuation theory of PDEs with random coefficients (2) Ergodic theory of SPDEs and (3) Exact solvability of SPDEs

    Updated on Jun 24, 2014 02:31 PM PDT
  3. Algebraic Topology

    Organizers: LEAD Jose Cantarero-Lopez (Centro de Investigación en Matemáticas), LEAD Michael Hill (University of Virginia)

    Modern algebraic topology is a broad and vibrant field which has seen recent progress on classical problems as well as exciting new interactions with applied mathematics. This summer school will consist of a series of lecture by experts on major research directions, including several lectures on applied algebraic topology. Participants will also have the opportunity to have guided interaction with the seminal texts in the field, reading and speaking about the foundational papers.

    Updated on Oct 13, 2014 01:24 PM PDT
  4. IAS/PCMI 2014: Mathematics and Materials

    Organizers: Mark Bowick (Syracuse University), David Kinderlehrer (Carnegie Mellon University), Govind Menon (Brown University), Charles Radin (University of Texas)

    The program in 2014 will bring together a diverse group of mathematicians and scientists with interests in fundamental questions in mathematics and the behavior of materials. The meeting addresses several themes including computational investigations of material properties, the emergence of long- range order in materials and self-assembly, the geometry of soft condensed matter and the calculus of variations, phase transitions and statistical mechanics. The program will cover several topics in discrete and differential geometry that are motivated by questions in materials science. Many central topics, such as the geometry of packings, problems in the calculus of variations and phase transitions, will be discussed from the complementary points of view of mathematicians and physicists.

    Updated on Mar 06, 2014 12:12 PM PST
  5. Dispersive Partial Differential Equations

    Organizers: Natasa Pavlovic (University of Texas), Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)

    The purpose of the workshop is to introduce graduate students to the recent developments in the area of dispersive partial differential equations (PDE).

    Dispersive equations have received a great deal of attention from mathematicians because of their applications to nonlinear optics, water wave theory and plasma physics. We will outline the basic tools of the theory that were developed with the help of multi-linear Harmonic Analysis techniques. The exposition will be as self-contained as possible.

    Updated on Jun 16, 2014 10:14 AM PDT
  6. Introduction to the Mathematics of Seismic Imaging

    Organizers: LEAD Gunther Uhlmann (University of Washington)

    In this two week program we will develop some of the mathematical foundations of seismic imaging that is a basic tool used in ``Imaging the Earth Interior". This is one of the components of the Mathematics of Planet Earth year in 2013.

    The goal in seismic imaging is to determine the inner structure of the Earth from the crust to the inner core by using information provided by earthquakes in the case of the deep interior or by measuring the reflection of waves produced by acoustic or elastic sources on the surface of the Earth. The mathematics of seismic imaging involves solving inverse problems for the wave equation. No previous experience on inverse problems will be assumed.

    Updated on Jul 25, 2013 09:45 AM PDT
  7. Mathematical General Relativity in Cortona, Italy

    Organizers: Justin Corvino (Lafayette College), Pengzi Miao (University of Miami), Giorgio Patrizio (Istituto Nazionale di Alta Matematica "Francesco Severi" (INdAM))

    In cooperation with INdAM (Istituto Nazionale di Alta Matematica) and the CMI (Clay Mathematical Institute), MSRI will sponsor a summer graduate workshop on Mathematical General Relativity in Cortona during the summer of 2013; the school will reprise the very successful school of Mathematical General Relativity held at MSRI in 2012.

    Mathematical general relativity is the study of mathematical problems related to Einstein's theory of gravitation. There are interesting connections between the physical theory and problems in differential geometry and partial differential equations.

    The purpose of the summer school is to introduce graduate students to some fundamental aspects of mathematical general relativity, with particular emphasis on the geometry of the Einstein constraint equations and the Positive Mass Theorem. These topics will comprise a component of the upcoming semester program at MSRI in Fall 2013.

    There will be mini-courses, as well as several research lectures.

    Updated on Aug 01, 2013 10:02 AM PDT
  8. New Geometric Techniques in Number Theory

    Organizers: Toby Gee (Imperial College, London), LEAD Ariane Mézard (Institut de Mathématiques de Jussieu), David Nadler (University of California, Berkeley), Peter Scholze (Universität Bonn)

    The branches of number theory most directly related to automorphic forms have seen enormous progress over the past five years. Techniques introduced since 2008 have made it possible to prove many new arithmetic applications. The purpose of the current workshop is to drow the attention of young students or researchers to new questions that have arisen in the course of bringing several chapters in the Langlands program and related algebraic number theory to a close. We will focus especially on some precise questions of a geometric nature, or whose solutions seem to require new geometric insights. A graduate level in Number Theory is expected.

    This two-week workshop will be devoted to the following subjects: Automorphy lifting theorems, p-adic local Langlands program, Characters of categorical representations and Hasse-Weil zeta function. During the first week, the lecturers present an open question and related mathematical objects. The first exercice sessions serve to direct the participants to an appropriate subject depending on their level. During the second week, the lecturers give some more advanced lectures on the field.

    Updated on Jul 02, 2013 10:48 AM PDT
  9. IAS/PCMI Summer 2013: Geometric Analysis

    Organizers: Hubert Bray (Duke University), Greg Galloway (University of Miami), Rafe Mazzeo (Stanford University), Natasa Sesum (Rutgers University)

    This Summer Graduate Workshop will be held in Park City, Utah.

    The Graduate Summer School bridges the gap between a general graduate education in mathematics and the specific preparation necessary to do research on problems of current interest. In general, these students will have completed their first year, and in some cases, may already be working on a thesis. While a majority of the participants will be graduate students, some postdoctoral scholars and researchers may also be interested in attending.

    We strongly recommend that graduate students have already had the equivalent of rigorous first year graduate-level courses in topology, algebra and analysis.

    The main activity of the Graduate Summer School will be a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures will not duplicate standard courses available elsewhere. Each course will consist of lectures with problem sessions. Course assistants will be available for each lecture series. The participants of the Graduate Summer School meet three times each day for lectures, with one or two problem sessions scheduled each day as well.

    Updated on May 06, 2013 11:06 AM PDT
  10. Seminaire de Mathematiques Superieures 2013: Physics and Mathematics of Link Homology

    Organizers: Sergei Gukov (California Institute of Technology), Mikhail Khovanov (Columbia University), Johannes Walcher (McGill University)

    This Summer Graduate Workshop will be held in Montreal, Canada.

    Homology theories of knots and links is a burgeoning field at the interface of mathematics with theoretical physics. The 2013 edition of the SMS will bring together leading researchers in mathematics and mathematical physics working in this area, with the aim to educate a new generation of scientists in this exciting subject. The school will provide a pedagogical review of the current state of the various constructions of knot homologies, and also encourage interactions between the communities in order to facilitate development of the unified picture.

    Updated on May 06, 2013 09:37 AM PDT
  11. Algebraic Topology

    Organizers: Andrew Blumberg (University of Texas), Teena Gerhardt (Michigan State University), LEAD Michael Hill (University of Virginia)

    Modern algebraic topology is a broad and vibrant field which has seen recent progress on classical problems as well as exciting new interactions with applied mathematics. This summer school will consist of a series of lecture by experts on major research directions, including several lectures on applied algebraic topology. Participants will also have the opportunity to have guided interaction with the seminal texts in the field, reading and speaking about the foundational papers.

    Updated on Jun 25, 2013 08:38 PM PDT
  12. Model Theory

    Organizers: David Marker* (University of Illinois, Chicago), Thomas Scanlon (University of California, Berkeley), Carol Wood (Wesleyan University).

    The workshop will consist of two minicourses, together with a selection of topical lectures.

    In the model theory course, o-minimality, and specifically the concrete example of the semi-algebraic sets of real numbers will provide the setting in which we introduce various fundamental results from model theory.
    The algebraic dynamics course will allow the introduction of concepts and proof techniques from number theory and algebraic geometry in the context of applications involving model theory.

    Toward the end of the workshop, the two minicourses will converge on the Pila-Wilkie theorem concerning points on analytic varieties, a result crucial in recent applications of o-minimality to diophantine geometry.

    Updated on Oct 15, 2014 05:17 AM PDT
  13. Mathematical General Relativity

    Organizers: Justin Corvino* (Lafayette College) and Pengzi Miao (University of Miami)

    Mathematical general relativity is the study of mathematical problems related to Einstein's theory of gravitation. There are interesting connections between the physical theory and problems in differential geometry and partial differential equations.

    The purpose of the workshop is to introduce graduate students to some fundamental aspects of mathematical general relativity, with particular emphasis on the geometry of the Einstein constraint equations and the Positive Mass Theorem. These topics will comprise a component of the upcoming semester program at MSRI in Fall 2013.

    There will be mini-courses, as well as several research lectures. Students are expected to have had courses in graduate real analysis and Riemannian geometry, while a course in graduate-level partial differential equations is recommended.

    Updated on Oct 03, 2014 12:27 PM PDT
  14. IAS/PCMI Summer 2012: Geometric Group Theory

    Organizers: Mladen Bestvina (University of Utah), Michah Sageev (Technion – Israel Institute of Technology), and Karen Vogtmann (Cornell University)

    This Summer Graduate Workshop will be held in Park City, Utah.

    Some mobility between the Research in Mathematics and Graduate Summer School programs is expected and encouraged, but interested candidates should read the guidelines carefully and apply to the one program best suited to their field of study and experience. Postdoctoral scholars who are working in the field of Geometric Group Theory should apply to the Research Program in Mathematics, not to the Graduate Summer School.
    Graduate students who are beyond their basic courses and recent PhDs in all fields of mathematics are encouraged to apply to the Graduate Summer School. Funding will go primarily to graduate students. Postdoctoral scholars not working in the field of Geometric Group Theory should also apply, but should be within four years of receipt of their PhD.
    Deadline for submission of applications is January 31, 2012. Supplemental materials (such as Reference Letters) must be received in the PCMI office by February 4, 2012. Please plan accordingly. (Late applications may be accepted at the discretion of the organizers.) Response may be expected in early April. Financial support is available. Applicants are invited to request financial support by checking the appropriate boxes on the application form.

    Updated on Mar 20, 2012 11:44 AM PDT
  15. Seminaire de Mathematiques Superieures 2012: Probabilistic Combinatorics

    Organizers: Louigi Addario-Berry* (McGill University), Luc Devroye (McGill University), Bruce Reed (McGill University)

    This Summer Graduate Workshop will be held in Montreal, Canada.

    One of the cornerstones of the probabilistic approach to solving combinatorial problems is the following guiding principle: information about global structure can be obtained through local analysis. This principle is ubiquitous in probabilistic combinatorics. It arises in problems ranging from graph colouring, to Markov chain mixing times, to Szemerédi's regularity lemma and its applications, to the theory of influences. The 2012 Séminaire de Mathématiques Supérieures brings together experts in probabilistic combinatorics from around the world, to explain cutting edge research which in one way or another exhibits this principle.

    Updated on May 07, 2013 11:14 PM PDT
  16. Noncommutative Algebraic Geometry

    Organizers: Dan Rogalski* (University of California, San Diego), Travis Schedler (Massachusetts Institute of Technology), Michael Wemyss (The University of Edinburgh, United Kingdom)

    This workshop will introduce some of the major themes of the MSRI program "Interactions between Noncommutative Algebra, Representation Theory, and Algebraic Geometry" to be held in the spring of 2013. There will be four mini-courses on the topics of noncommutative projective geometry, deformation theory, noncommutative resolutions of singularities, and symplectic reflection algebras. As well as providing theoretical background, the workshop will aim to equip participants with some intuition for the many open problems in this area through worked examples and experimental computer calculations.

    Updated on Nov 13, 2014 08:50 AM PST
  17. Cluster Algebras and Cluster Combinatorics

    Organizers: Gregg Musiker (University of Minnesota), Lauren Williams* (University of California, Berkeley)

    Cluster algebras are a class of combinatorially defined rings that provide a unifying structure for phenomena in a variety of algebraic and geometric contexts. A partial list of related areas includes quiver representations, statistical physics, and Teichmuller theory. This summer workshop for graduate students will focus on the combinatorial aspects of cluster algebras, thereby providing a concrete introduction to this rapidly-growing field. Besides providing background on the fundamentals of cluster theory, the summer school will cover complementary topics such as total positivity, the polyhedral geometry of cluster complexes, cluster algebras from surfaces, and connections to statistical physics. No prior knowledge of cluster algebras will be assumed.

    The workshop will consist of four mini-courses with accompanying tutorials. Students will also have opportunities for further exploration using computer packages in Java and Sage.

    Updated on Sep 04, 2014 10:16 AM PDT
  18. Toric Varieties in Cortona, Italy

    Organizers: Scientific Committee: David Cox* (Amherst College) and Hal Schenck (University of Illinois)
    Organizing Committee: Giorgio Patrizio (Università di Firenze, Italy) and Sandro Verra (Università di Roma Tre, Italy)

    In cooperation with INdAM (Istituto Nazionale di Alta Matematica) and the SMI (Scuola Matematica Interuniversitaria), MSRI will sponsor a summer graduate workshop (SGW) on toric varieties in Cortona during summer of 2011; the workshop will reprise the very successful SGW on toric varieties held at MSRI in 2009.
    Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by glueing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.

    Special restrictions apply, please see the workshop homepage.

    Updated on May 07, 2013 11:14 PM PDT
  19. Geometric Measure Theory and Applications

    Organizers: Camillo De Lellis (Universität Zürich), Tatiana Toro* (University of Washington)

    Geometric Measure Theory (GMT) is a field of Mathematics that has contributed greatly to the development of the calculus of variations and geometric analysis. In recent years it has experienced a new boom with the development of GMT in the metric space setting which has lead to unexpected applications (for examples to questions arising from theoretical computer sciences). The goal of this summer graduate workshop is to introduce students to different aspects of this field. There will be 5 mini-courses and a couple of research lectures. We expect students to have a solid background in measure theory.

    Updated on Aug 19, 2014 10:21 AM PDT
  20. IAS-PCMI Summer School on Moduli Spaces of Riemann Surfaces

    Organizers: Benson Farb (University of Chicago), Richard Hain (Duke University), and Eduard Looijenga (University of Utrecht, Netherlands)

    The study of moduli spaces of Riemann surface is a rich mixture of geometric topology, algebraic topology, complex analysis and algebraic geometry. Each community of researchers that studies these moduli spaces generates its own problems and its own techniques for solving them. However, it is not uncommon for researchers in one community to solve problems generated by another once they become aware of them. The goal of this summer school is to give graduate students a broad background in the various approaches to the study of moduli spaces of Riemann surfaces so that they will be aware of the problems and techniques of many of the communities that study these fascinating objects. Graduate student participants from the various communities will be encouraged to interact with their colleagues from the other communities of students in order to maximize cross fertilization.

    Special restrictions apply, please see the workshop homepage.

    Updated on Apr 27, 2011 06:34 AM PDT
  21. Seminaire de Mathematiques Superieures 2011. Metric Measure Spaces: Geometric and Analytic Aspects.

    Organizers: Galia Dafni* (Concordia University, Montreal), Robert McCann (University of Toronto), and Alina Stancu (Concordia University, Montreal)

    In cooperation with the CRM (Centre de Recherches Mathematiques), the Fields Institute, and the PIMS (Pacific Insitute for Mathematical Sciences), MSRI will sponsor a summer graduate workshop on Metric measure spaces: geometric and analytic aspects in Montreal, Canada.
    In recent decades, metric-measure spaces have emerged as a fruitful source of mathematical questions in their own right, and as indispensable tools for addressing classical problems in geometry, topology, dynamical systems and partial differential equations. The purpose of the 2011 summer school is to lead young scientists to the research frontier concerning the analysis and geometry of metric-measure spaces, by exposing them to a series of mini-courses featuring leading researchers who will present both the state-of-the-art and the exciting challenges which remain.

    Special restrictions apply, please see the workshop homepage.

    Updated on May 07, 2013 11:14 PM PDT
  22. The Dirichlet Space: Connections between Operator Theory, Function Theory, and Complex Analysis

    Organizers: Nicola Arcozzi (Universita' di Bologna), Richard Rochberg (Washington University), Eric T Sawyer (McMaster University), Brett D Wick* (Georgia Institute of Technology)

    This workshop will focus on the classical Dirichlet space of holomorphic functions on the unit disk. This space is at the center of several active, interrelated areas of research that, viewed more broadly, focus on the interaction between function theoretic operator theory and potential theory. There are several goals of this Summer Graduate Workshop. First, mathematically, the workshop will demonstrate the basic properties of the Dirichlet space, then introduce the technique of Trees in Function Spaces. The workshop will show the interconnections between the areas of Complex Analysis, Function Theory, and Operator Theory and will also illustrate the real-variable analogues of the analytic result discussed.

    Updated on Sep 12, 2013 10:19 AM PDT
  23. Commutative Algebra

    Organizers: Daniel Erman (Stanford University), Irena Swanson* (Reed College), and Amelia Taylor (Colorado College)

    This workshop will involve a combination of theory and symbolic computation in commutative algebra. The lectures are intended to introduce three active areas of research: Boij-Söderberg theory, algebraic statistics, and integral closure. The lectures will be accompanied with tutorials on the computer algebra system Macaulay 2.

    Updated on Nov 27, 2014 08:59 PM PST
  24. Algebraic, Geometric, and Combinatorial Methods for Optimization

    Organizers: Matthias Köppe (University of California, Davis) and Jiawang Nie (University of California, San Diego)

    This workshop is intended to introduce to graduate students the main ideas of algebraic, geometric and combinatorial methods in global optimization. We emphasize the major developments in the past few years from two viewpoints. The first one is that of the interaction of semidefinite programming and real algebraic geometry and includes topics such as linear matrix inequalities, positive polynomials, and sums of squares. The second viewpoint is that of primal methods and generating function methods in integer linear and nonlinear optimization.

    Updated on Nov 04, 2014 11:54 AM PST
  25. Mathematics of Climate Change

    Organizers: Chris Jones (University of North Carolina and University of Warwick), Doug Nychka (National Center for Atmospheric Research), and Mary Lou Zeeman (Bowdoin College)

    NCAR supports scientific research on nearly every aspect of the atmosphere and related components of the Earth’s physical and biological systems. This includes developing state-of-the- art climate models, high performance computing and also innovative ways of observing the atmosphere and oceans. The Center has approximately 1000 staff and is supported primarily by the National Science Foundation. Part of the NCAR mission is to engage students in the problems of understanding climate and weather and so provides an ideal context for this summer graduate workshop. The workshop is also part a larger program at NCAR through the Institute for Mathematics Applied to Geosciences: Mathematicians and Climate.
    For more information, please see NCAR summer school page

    Updated on Jun 25, 2014 11:37 AM PDT
  26. IAS/PCMI Research Summer School 2010: Image Processing

    Organizers: Tony Chan (University of California, Los Angeles), Ron Devore (Unversity of South Carolina, Columbia), Stanley Osher (University of California, Los Angeles), and Hongkai Zhao (University of California, Irvine)

    Both an MSRI nomination and PCMI application are required to attend the Image Processing summer school. The application form can be found by going to the PCMI page IAS/PCMI application homepage and clicking on the sentence "You're ready to apply."




    Once the PCMI application is complete IAS/PCMI application homepage please return a letter of nomination from the Director of Graduate Studies to MSRI.

    Updated on Dec 04, 2013 01:28 PM PST
  27. Probability workshop: 2010 PIMS Summer School in Probability.

    Organizers: Krzysztof Burdzy (University of Washington), Zhenqing Chen (University of Washington), Christopher Hoffman (University of Washington), Soumik Pal (University of Washington), Yuval Peres ( University of California, Berkeley)

    The 2010 Pacific Institute for the Mathematical Sciences (PIMS) Summer
    School in Probability will be held at the University of Washington and
    Microsoft Research. The workshop will have two main courses, and three short ones.

    For further information please visit the following link pims homepage

    Updated on Aug 19, 2014 10:57 AM PDT
  28. Sage Days 22: Computing with Elliptic Curves

    Organizers: William Stein (University of Washington)

    This workshop will introduce graduate students to several central ideas in the arithmetic of elliptic curves. Participants will join a project group that will focus mainly on one topic, possibly involving elliptic curves over number fields, complex or p-adic L-functions, Heegner points and Kolyvagin classes, Iwasawa theory, and the Birch and Swinnerton-Dyer conjecture. The workshop will emphasize the essential interplay of abstract mathematics with explicit computation, which has played a central role in number theory ever since Birch and Swinnerton-Dyer made their famous conjecture in the 1960s. Participants will use, and improve, the free open-source Python-based mathematical software system Sage (http://www.sagemath.org) for computational projects.

    Updated on Nov 26, 2014 04:19 PM PST
  29. Summer School on Operator Algebras and Noncommutative Geometry

    Organizers: Heath Emerson, (University of Victoria) Thierry Giordano, (University of Ottawa) Marcelo Laca*, (University of Victoria) Ian Putnam, (University of Victoria)

    The summer school aims to expose participants to the classi cation of noncommutative
    spaces, to the study of their homological and cohomological invariants, and to explore fascinating
    new connections between their symmetries and long standing problems in number
    theory. Additional information can be found on the PIMS page

    Updated on Aug 08, 2014 03:33 PM PDT
  30. Summer Graduate Workshop: Symplectic and Contact Geometry and Topology

    Organizers: John Etnyre (Georgia Institute of Technology), Dusa McDuff* (Barnard College, Columbia University) and Lisa Traynor (Bryn Mawr College).

    Symplectic and Contact Topology has undergone rapid and exciting growth
    in the past few decades and is currently a rich subject, employing a variety of diverse techniques and touching on many areas of mathematics, such as algebraic and differential geometry, dynamical systems and low dimensional topology. This workshop is intended both for graduate students new to the
    area and for those working in the field.
    Lectures in the first week will introduce participants to basic topological, geometric and analytic techniques, including J-holomorphic curves. The second week will discuss applications to symplectic geometry and to 3-dimensional topology and knot theory. A variety of discussion
    sessions in the afternoon will cater to the differing interests of the students. Participants may consider staying for the Connections for Women and/or the Introductory workshop to the year long Symplectic Geometry program that starts just after this workshop.

    Updated on Nov 05, 2014 09:10 AM PST
  31. Inverse Problems

    Organizers: Gunther Uhlmann* (University of Washington).

    Inverse Problems are problems where causes for a desired or an observed effect are to be determined. They lie at the heart of scientific inquiry and technological development. Applications include a number of medical as well as other imaging techniques, location of oil and mineral deposits in the earth's substructure, creation of astrophysical images from telescope data, finding cracks and interfaces within materials, shape optimization, model identification in growth processes and, more recently, modelling in the life sciences.

    The workshop will consist of several minicourses addressing several of the theoretical and practical issues arising in inverse problems including boundary rigidity and travel time tomography, cloaking and invisibility, electrical impedance imaging, statistical methods and biological applications, thermoacoustic and x-ray tomography, and resonances.

    Updated on Aug 14, 2014 02:45 PM PDT
  32. Computational Theory of Real Reductive Groups (Salt lake City)

    Organizers: Jeffrey Adams (University of Maryland) , Peter Trapa* (University of Utah), Susana Salamanca (New Mexico State University), John Stembridge (University of Michigan), and David Vogan (MIT).

    The structure of real reductive algebraic groups is controlled by a remarkably simple combinatorial framework, generalizing the presentation of Coxeter groups by generators and relations. This framework in turn makes much of the infinite-dimensional representation theory of such groups amenable to computation.

    The Atlas of Lie Groups and Representations project is devoted to looking at representation theory from this computationally informed perspective. The group (particularly Fokko du Cloux and Marc van Leeuwen) has written computer software aimed at supporting research in the field, and at helping those who want to learn the subject.

    The workshop will explore this point of view in lecture series aimed especially at graduate students and postdocs with only a modest background (such as the representation theory of compact Lie groups).

    Deadline for funding applications: 1 March, 2009.

    The official workshop website is at: http://www.liegroups.org/workshop/

    Updated on Nov 26, 2008 06:58 AM PST
  33. Random Matrix theory

    Organizers: Jinho Baik ( University of Michigan), Percy Deift* (New York University),Toufic Suidan (University of Arizona), Brian Rider (University of Colorado)

    The goal of this workshop is two-fold: (1) to describe many of the recent advances that have been made in the application of random matrix theory to problems in mathematics and physics (2) to develop some of the mathematical tools that are needed to enter the field. Applications of random matrix theory are now being made to number theory, combinatorics, statistical physics and statistics amongst other fields. The techniques employed in the field include methods from integrable systems, combinatorics, complex analysis, orthogonal polynomials and of course random matrix theory per se.

    Updated on Aug 01, 2014 05:17 PM PDT
  34. Toric Varieties

    Organizers: David Cox ( Amherst College) and Hal Schenck (University of Illinois)

    Toric varieties are algebraic varieties defined by combinatorial data, and there is a wonderful interplay between algebra, combinatorics and geometry involved in their study. Many of the key concepts of abstract algebraic geometry (for example, constructing a variety by gluing affine pieces) have very concrete interpretations in the toric case, making toric varieties an ideal tool for introducing students to abstruse concepts.

    Updated on Nov 27, 2014 08:59 PM PST
  35. Climate Change - Summer Graduate Workshop

    Organizers: Christopher Jones (UNC Chapel Hill and U Warwick, UK), Inez Fung (U.C. Berkeley), Eric Kostelich (Arizona State University), K.K. Tung (U. Washington), and Mary Lou Zeeman (Bowdoin College), Charles D. Camp (Cal Poly, San Luis Obispo), Rachel Kuske (Univ British Columbia)

    The goal of the workshop will be to discern ways in which mathematics can contribute and to expose new researchers to some of the key areas that we believe will form the basis of serious mathematical considerations of climate change issues.

    Updated on Sep 08, 2014 03:02 PM PDT
  36. Geometry and Representation Theory of Tensors for Computer Science, Statistics, and other areas

    Organizers: J.M. Landsberg (Texas A&M), Lek-Heng Lim (UC Berkeley) and Jason Morton (UC Berkeley)

    Recently the common geometry of tensors arising in questions in computational complexity, statistical learning theory, signal processing, scientific data analysis have been looked at from a unified perspective. The underlying geometry and representation theory will be covered in this workshop with and eye towards problems such as the complexity of matrix multiplication, Valiant's approach to P=NP, measures of entanglement in quantum information theory, graphicalmodels in statistical learning theory, independent component analysis and other multilinear data analytic techniques.

    Updated on Jul 03, 2014 04:41 PM PDT
  37. A Window into Zeta and Modular Physics

    Organizers: Floyd Williams (University of Massachusetts) and Klaus Kirsten (Baylor University)

    In recent years,a noteworthy and very fruitful interlacing of number theory and physics has emerged.As indicated in the September 2007 issue of the AMS Notices,for example,a new journal "Communications in Number Theory and Physics " has just been launched to follow significant interactions and dynamics between these two fields.Several books are now available,in addition to an array of conference and workshop activity,that accent this fortunate merger of "pure"mathematics and physical theory-with applications that range from field theory (conformal and topological),extended objects (strings and branes)cosmology and black hole physics, to Bose-Einstein condensation and the theory of relativistic gases.

    Updated on Sep 02, 2014 10:54 AM PDT
  38. Deformation Theory and Moduli in Algebraic Geometry

    Organizers: Max Lieblich (Princeton), Martin Olsson (Berkeley), Brian Osserman (Berkeley), Ravi Vakil (Stanford)

    This workshop is intended to introduce to graduate students the main ideas of deformation theory and moduli spaces in algebraic geometry. We hope to illuminate the general theory through extensive discussions of concrete examples and applications.

    Updated on Nov 27, 2014 05:31 PM PST
  39. Derived Categories in Algebraic Geometry

    Organizers: Aaron Bertram (University of Utah), Y.P. Lee (university of Utah), Eric Sharpe (University of Utah and Virginia Tech)

    Updated on Jul 14, 2014 10:18 AM PDT
  40. Summer Graduate Workshop in Computational Number Theory

    Organizers: William Stein (University of Washington)

    This workshop will concentrate on computing with modular forms, providing students with the necessary background in both the theoretical and computational aspects of the subject.

    Updated on Oct 27, 2014 06:16 PM PDT
  41. Data Assimilation for the Carbon Cycle

    Organizers: Inez Fung (University of California, Berkeley)

    Projections of future climate require projections of the abundance of carbon dioxide and other trace constituents in the atmosphere. This in turns requires understanding the sources and sinks of atmospheric CO2 and how they interact with the climate. Participants will work on projects using atmospheric data provided by NCAR.

    Updated on Jul 03, 2014 04:41 PM PDT
  42. IAS/PCMI Summer Program: Low Dimensional Topology

    Organizers: Peter Oszvath (Columbia University) and Tom Mrowka (MIT).

    This will be a minicourse for graduate students on recent techniques and advances in three and four dimensional topology.

    Updated on Nov 07, 2014 12:17 PM PST
  43. MSRI Summer Graduate Workshop: Mathematical aspects of computational biology

    Organizers: Reinhard Laubenbacher (Virginia Bioinformatics Institute at Virginia Tech) and Lior Pachter (Department of Mathematics, UC Berkeley)

    The novel features of biological systems pose new challenges that require new mathematics. In many cases even the fundamental mathematical language is lacking in order to treat certain biological phenomena quantitatively. Here, traditionally non-applied areas of mathematics can make an important contribution, and at the same time take advantage of unique new problems to open up mathematically interesting avenues of research.

    Updated on Sep 09, 2014 08:33 AM PDT
  44. SL(2,R), a Minicourse at the University of Utah

    Organizers: Bill Casselman (University of British Columbia), Dragan Milicic (University of Utah), Peter Trapa (University of Utah)

    This minicourse will be aimed at beginning graduate students, and is devoted to all aspects of the theory of SL(2,R) including: discrete and principal series, intertwining operators, unitary representations, character theory, etc.

    Updated on Jun 25, 2014 12:56 PM PDT
  45. Mathematical Graphics

    Organizers: David Austin, Bill Casselman and Jim Fix

    Updated on Dec 01, 2008 06:02 AM PST
  46. Graduate Student Warm-Up Workshop in Algebraic Geometry

    Organizers: Sándor Kovács, Tony Pantev, and Ravi Vakil

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

    Updated on Dec 01, 2008 06:03 AM PST
  47. Hyperplane Arrangements and Applications

    Organizers: Sergey Yuzvinsky

    This MSRI Summer Graduate Program at the University of Oregon will provide an introduction to the material to be covered in the fall, 2004 MSRI program on Hyperplane Arrangements and Applications. See the program page for more information on the content.

    Updated on Feb 12, 2007 09:42 AM PST
  48. Mathematical Graphics

    Organizers: Bill Casselman and David Austin

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

    Updated on Feb 12, 2007 09:47 AM PST
  49. Biomathematics, Bioengineering & Clinical Aspects of Blood Flow

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

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

    Updated on Feb 12, 2007 09:45 AM PST
  50. Excursions in Computational Number Theory -- Polynomials with Integer Coefficients

    Organizers: Peter Borwein and Michael Filaseta

    Summer Graduate Program -- open only to students nominated by MSRI's Academic Sponsor universities, to be held in Vancouver, BC, Canada at the Pacific Institute of Mathematics facility of Simon Fraser University.

    Updated on Feb 12, 2007 09:44 AM PST
  51. Cryptography

    Organizers: Neal Koblitz, Alfred Menezes

    Updated on Feb 12, 2007 09:47 AM PST
  52. Random Walk and Geometry

    Organizers: Persi Diaconis, Laurent Saloff-Coste

    Updated on Feb 12, 2007 09:45 AM PST
  53. Hyperbolic Geometry

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

    Updated on Feb 12, 2007 09:47 AM PST
  54. Mathematical Biology

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

    Updated on Feb 23, 2007 08:45 AM PST
  55. 4-Manifolds

    Organizers: Rob Kirby, Ron Stern

    Updated on May 17, 2007 06:46 AM PDT