
Chip Firing and Tropical Curves
Organizers: LEAD Matthew Baker (Georgia Institute of Technology), David Jensen (University of Kentucky), Sam Payne (Yale University)Tropical geometry uses a combination of techniques from algebraic geometry, combinatorics, and convex polyhedral geometry to study degenerations of algebraic varieties; the simplest tropical objects are tropical curves, which one can think of as "shadows" of algebraic curves. Linear equivalence of divisors on an abstract tropical curve is determined by a simple but rich combinatorial process called "chip firing", which was discovered independently in the discrete setting by physicists and graph theorists. From a pedagogical point of view, one can view tropical curves as a combinatorial model for the highly analogous but more abstract theory of algebraic curves, but there is in fact much more to the story than this: one can use tropical curves and chip firing to prove theorems in algebraic geometry and number theory. This field is relatively new, so participants will have the opportunity to start from scratch and still get a glimpse of the cutting edge in this active research area.
Updated on Aug 30, 2016 03:39 PM PDT 
Electronic Structure Theory
Organizers: LEAD Lin Lin (University of California, Berkeley), Jianfeng Lu (Duke University), James Sethian (University of California, Berkeley)Ab initio or first principle electronic structure theories, particularly represented by KohnSham density functional theory (KSDFT), have been developed into workhorse tools with a wide range of scientific applications in chemistry, physics, materials science, biology etc. What is needed are new techniques that greatly extend the applicability and versatility of these approaches. At the core, many of the challenges that need to be addressed are essentially mathematical. The purpose of the workshop is to provide graduate students a selfcontained introduction to electronic structure theory, with particular emphasis on frontier topics in aspects of applied analysis and numerical methods.
Updated on Jul 27, 2016 04:16 PM PDT 
An Introduction to Character Theory and the McKay Conjecture
Organizers: Robert Guralnick (University of Southern California), Pham Tiep (University of Arizona)Character Theory of Finite Groups provides one of the most powerful tools to study groups. In this course we will give a gentle introduction to basic results in the Character Theory, as well as some of the main conjectures in Group Representation Theory, with particular emphasis on the McKay Conjecture.
Updated on Jul 22, 2016 02:27 PM PDT 
Mixed Integer Nonlinear Programming: Theory, algorithms and applications
Organizers: Francisco Castro (University of Sevilla), Elena Fernandez (Universitat Politecnica de Catalunya), Justo Puerto (University of Sevilla)This school is oriented to the presentation of theory, algorithms and applications for the solution of mixed integer nonlinear problems (MINLP). This type of problems appears in numerous application areas where the modelization of nonlinear phenomena with logical constraints is important; we must remember here the memorable phrase “the world is nonlinear”. Nowadays the theoretical aspects of this area are spread in a number of recent papers which makes it difficult, for nonspecialist, to have a solid background of the existing results and new advances in the field. This school aims to organize and present this material in an organized way. Moreover, it also pursues to link theory with actual applications. In particular, remarkable applications can be found in air traffic control agencies, the air companies, the electric power generation companies, the chemical complex units, the analysis of financial products usually associated with risk dealing and in the algorithms in the statistical field and artificial intelligence as for instance artificial neural networks, or supporting vector machines, among many others.
Updated on May 17, 2016 10:51 AM PDT 
Harmonic Analysis and Elliptic Equations on real Euclidean Spaces and on Rough Sets
Organizers: LEAD Steven Hofmann (University of Missouri), Jose Maria Martell (Instituto de Ciencias Matematicas (ICMAT))The goal of the workshop is to present harmonic analysis techniques in $R^n$ (the ``flat" setting), and then to show how those techniques extend to much rougher settings, with application to the theory of elliptic equations. Thus, the subject matter of the workshop will introduce the students to an active, current research area: the interface between harmonic analysis, elliptic PDE, and geometric measure theory.
Updated on Aug 05, 2016 10:47 AM PDT 
Seminaire de Mathematiques Superieures 2016: Dynamics of Biological Systems
Organizers: Thomas Hillen (University of Alberta), Mark Lewis (University of Alberta), Yingfei Yi (University of Alberta)The purpose of this summer school is to focus on the interplay of dynamical and biological systems, developing the rich connectionbetween science and mathematics that has been so successful to date. Our focus will be on understanding the mathematical structure of dynamical systems that come from biological problems, and then relating the mathematical structures back to the biology to provide scientific insight. We will focus on five key areas: complex bionetworks, multi scale biological dynamics, biological waves, nonlinear dynamics of pattern formation, and disease dynamics. For each of the five key areas, we will invite 23 world leaders who are also excellent communicators to deliver a series of 24 onehour lectures. We expect an average of eight hours of lecture per subject area, spread over approximately two weeks.
Updated on Nov 11, 2015 03:54 PM PST 
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 stateoftheart methods and results in mathematical fluid dynamics. In the first week, we will discuss the mathematical foundations and modern analysis aspects of the NavierStokes 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 31, 2015 11:47 AM PDT 
Gaps between Primes and Analytic Number Theory
Organizers: Dimitris Koukoulopoulos (Université de Montréal), LEAD Emmanuel Kowalski (ETH Zuerich), 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 Aug 05, 2016 10:41 AM PDT 
Berkeley summer course in mining and modeling of neuroscience data
Organizers: Ingrid Daubechies (Duke University), Bruno Olshausen (University of California, Berkeley), Christos Papadimitriou (University of California, Berkeley), Fritz Sommer (University of California, Berkeley), LEAD Jeff Teeters (University of California, Berkeley)This course is for students and researchers with backgrounds in mathematics and computational sciences who are
interested in applying their skills toward problems in neuroscience. It will introduce the major open questions of
neuroscience and teach stateof–theart techniques for analyzing and modeling neuroscience data sets. The course is designed for students at the graduate level and researchers with background in a quantitative field such as
engineering, mathematics, physics or computer science who may or may not have a specific neuroscience
background. The goal of this summer course is to help researchers find new exciting research areas and at the same time to strengthen quantitative expertise in the field of neuroscience. The course is sponsored by the National Science Foundation from a grant supporting activities at the data sharing repository CRCNS.org, the Helen Wills
Neuroscience Institute, the Simons Institute for the Theory of Computing and the Mathematical Science Research
Institute.Updated on Feb 23, 2015 03:59 PM PST 
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 temporalspatial behaviors. This will be a very handson workshop with students working alone and in teams to program and present key ideas.
Updated on Jun 03, 2015 12:21 PM PDT 
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 
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 Jan 28, 2015 10:59 AM PST 
Geometric Group Theory
Organizers: LEAD John Mackay (University of Bristol), Anne Thomas (University of Sydney), 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 Jul 06, 2015 03:14 PM PDT 
CRMPIMS Summer School in Probability
Organizers: LEAD Louigi AddarioBerry (McGill University), LouisPierre Arguin (University of Montreal), Alexander Fribergh (University of Montreal), Lea Popovic (Concordia University)The 2015 CRMPIMS Summer School in Probability will take place in Montreal, Canada, from June 15July 11, 2015. The school is built around two principal 24hour lecture courses, which will be delivered by Alice Guionnet (random matrices, free probability and the enumeration of maps) and Remco van der Hofstad (highdimensional percolation and random graphs). There will additionally be minicourses by Louigi AddarioBerry (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 Apr 12, 2016 04:17 PM PDT 
Geometry and Analysis
Organizers: HansJoachim Hein (Imperial College, London), LEAD Aaron Naber (Northwestern University)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, KahlerEinstein manifolds, and the analysis of Riemann surfaces.
Updated on Aug 05, 2016 10:38 AM PDT 
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 stateoftheart 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 SPDEsUpdated on Aug 05, 2016 10:40 AM PDT 
Algebraic Topology
Organizers: LEAD Jose CantareroLopez (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.
Videos of selected lectures may be found here.
Updated on Jan 15, 2015 11:27 AM PST 
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 selfassembly, 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 
Seminaire de Mathematiques Superieures 2014: Counting Arithmetic Objects
Organizers: Henri Darmon (McGill University), Andrew Granville (Université de Montréal), Benedict Gross (Harvard University)Updated on Jan 16, 2014 08:48 AM PST 
Dispersive Partial Differential Equations
Organizers: Natasa Pavlovic (University of Texas), Nikolaos Tzirakis (University of Illinois at UrbanaChampaign)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 multilinear Harmonic Analysis techniques. The exposition will be as selfcontained as possible.
Updated on Jun 16, 2014 10:14 AM PDT 
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 
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 minicourses, as well as several research lectures.
Updated on Aug 01, 2013 10:02 AM PDT 
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 twoweek workshop will be devoted to the following subjects: Automorphy lifting theorems, padic local Langlands program, Characters of categorical representations and HasseWeil 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 
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 graduatelevel 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 
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 
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 
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, ominimality, and specifically the concrete example of the semialgebraic 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 PilaWilkie theorem concerning points on analytic varieties, a result crucial in recent applications of ominimality to diophantine geometry.
Updated on Feb 10, 2017 03:15 PM PST 
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 minicourses, as well as several research lectures. Students are expected to have had courses in graduate real analysis and Riemannian geometry, while a course in graduatelevel partial differential equations is recommended.
Updated on Aug 03, 2016 05:06 AM PDT 
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 
Seminaire de Mathematiques Superieures 2012: Probabilistic Combinatorics
Organizers: Louigi AddarioBerry* (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 
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 minicourses 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 Aug 03, 2016 05:06 AM PDT 
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 rapidlygrowing 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 minicourses with accompanying tutorials. Students will also have opportunities for further exploration using computer packages in Java and Sage.
Updated on Jan 04, 2017 12:32 PM PST 
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 
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 minicourses and a couple of research lectures. We expect students to have a solid background in measure theory.
Updated on Feb 23, 2017 10:57 AM PST 
IASPCMI 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 
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, metricmeasure 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 metricmeasure spaces, by exposing them to a series of minicourses featuring leading researchers who will present both the stateoftheart and the exciting challenges which remain.
Special restrictions apply, please see the workshop homepage.
Updated on May 07, 2013 11:14 PM PDT 
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 realvariable analogues of the analytic result discussed.
Updated on Sep 12, 2013 10:19 AM PDT 
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: BoijSöderberg theory, algebraic statistics, and integral closure. The lectures will be accompanied with tutorials on the computer algebra system Macaulay 2.
Updated on Feb 27, 2017 07:52 AM PST 
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 Feb 10, 2017 03:15 PM PST 
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 stateofthe 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 pageUpdated on Feb 10, 2016 05:02 PM PST 
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 Feb 10, 2017 03:15 PM PST 
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 Dec 12, 2016 11:05 AM PST 
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 padic Lfunctions, Heegner points and Kolyvagin classes, Iwasawa theory, and the Birch and SwinnertonDyer 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 SwinnertonDyer made their famous conjecture in the 1960s. Participants will use, and improve, the free opensource Pythonbased mathematical software system Sage (http://www.sagemath.org) for computational projects.
Updated on Feb 13, 2017 08:45 AM PST 
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 classication 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 pageUpdated on Dec 22, 2015 04:00 PM PST 
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 Jholomorphic curves. The second week will discuss applications to symplectic geometry and to 3dimensional 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 Feb 28, 2017 12:56 PM PST 
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 xray tomography, and resonances.
Updated on Aug 03, 2016 05:05 AM PDT 
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 infinitedimensional 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 
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 twofold: (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 Feb 25, 2017 09:59 AM PST 
IAS/PCMI Summer Program: The Arithmetic of Lfunctions
Organizers: Cristian Popescu (UCSD), Karl Rubin ( UC Irvine) , Alice Silverberg (UC Irvine).For application forms and information please visit the following link IAS/PCMI application homepage
Updated on Nov 26, 2008 06:58 AM PST 
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 Feb 27, 2017 07:52 AM PST 
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 
Geometry and Representation Theory of Tensors for Computer Science, Statistics, and other areas
Organizers: J.M. Landsberg (Texas A&M), LekHeng 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 Aug 03, 2016 05:06 AM PDT 
IAS/PCMI Summer Program: Analytic and Algebraic Geometry: Common Problems  Different Methods
Organizers: Mircea Mustaţă (University of Michigan), Jeff McNeal (Ohio State University)NOTE: This workshop requires a special application with a January 20, 2008 deadline. For application forms, please visit http://www.admin.ias.edu/ma/current/program_gradsummer.php
Updated on Aug 03, 2016 05:05 AM PDT 
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 theorywith applications that range from field theory (conformal and topological),extended objects (strings and branes)cosmology and black hole physics, to BoseEinstein condensation and the theory of relativistic gases.
Updated on Feb 21, 2017 08:27 AM PST 
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 Feb 10, 2017 03:15 PM PST 
Continuous Optimization and Applications
Organizers: Henry Wolkowicz. (University of Waterloo)Updated on Dec 19, 2013 01:40 PM PST 
Summer Graduate Workshop on Data Assimilation for the Carbon Cycle
Updated on Dec 01, 2008 02:26 AM PST 
IAS/PCMI summer conference: Statistical Mechanics
Organizers: Scott Sheffield, Thomas SpencerUpdated on Dec 01, 2008 02:24 AM PST 
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 Aug 03, 2016 05:05 AM PDT 
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 Feb 17, 2017 02:46 PM PST 
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 
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 Dec 09, 2016 04:49 PM PST 
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 nonapplied 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 Feb 10, 2017 03:15 PM PST 
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 
Computing the Continuous Discretely: Integer Point Enumeration in Polyhedra (Summer Graduate Workshop)
Organizers: Mathias Beck and Sinai RobinsUpdated on Feb 12, 2007 09:39 AM PST 
CR Geometry: Complex Analysis Meets Real Geometry and Number Theory
Organizers: John D’AngeloUpdated on Nov 24, 2015 04:52 PM PST 
AMSIMSSIAM Summer School in Commutative Algebra: Local Cohomology and Its Applications
Organizers: Anurag Singh and Uli WaltherGraduate Students from MSRI Sponsoring Institutions may benominated to participate in this program.
Updated on Dec 01, 2008 06:01 AM PST 
Clay Mathematics Institute 2005 Summer School Ricci Flow, 3 Manifolds And Geometry
Organizers: Gang Tian, John Lott, John Morgan, Bennett Chow, Tobias Colding, Jim Carlson, David Ellwood, Hugo RossiGraduate Students from MSRI Sponsoring Institutions may benominated to participate in this program.
Updated on Nov 25, 2016 09:42 AM PST 
Mathematical Graphics
Organizers: David Austin, Bill Casselman and Jim FixUpdated on Dec 01, 2008 06:02 AM PST 
Graduate Student WarmUp Workshop in Algebraic Geometry
Organizers: Sándor Kovács, Tony Pantev, and Ravi VakilGraduate Students from MSRI Sponsoring Institutions may benominated to participate in this program.
Updated on Dec 01, 2008 06:03 AM PST 
Knot Theory and 3Manifolds (Summer Graduate Workshop)
Organizers: S. Boyer (UQAM), R. Fenn (Sussex), D. Rolfsen, Chair (UBC), D. Sjerve (UBC)Updated on Dec 08, 2013 06:22 PM PST 
Hyperplane Arrangements and Applications
Organizers: Sergey YuzvinskyThis 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 
Triangulations of Point Sets: Applications, Structures, Algorithms
Organizers: Jesús A. De Loera, Jörg Rambau, and Francisco SantosPlease note, MSRI's Summer Graduate Programs are open only to students nominated by MSRI's Academic Sponsor universities.
Updated on May 13, 2013 11:00 PM PDT 
Mathematical Graphics
Organizers: Bill Casselman and David AustinPlease 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 
Biomathematics, Bioengineering & Clinical Aspects of Blood Flow
Organizers: Stanley A. Berger, Giovanni P. Galdi (cochair), Charles S. Peskin, Alfio Quarteroni, Anne M. Robertson (cochair), Adélia Sequeira, and Howard YonasSummer Graduate Program  open only to students nominated by MSRI's Academic Sponsor universities.
Updated on Feb 12, 2007 09:45 AM PST 
Excursions in Computational Number Theory  Polynomials with Integer Coefficients
Organizers: Peter Borwein and Michael FilasetaSummer 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 
Combinatorial Game Theory (Summer Graduate Workshop II)
Organizers: Elwyn Berlekamp and David WolfeUpdated on Feb 07, 2007 06:04 AM PST 
MSRI/PMMB Short Course: Mathematical and Computational Challenges in Molecular and Cell Biology
Organizers: Nicholas R. Cozzarelli, Michael Levitt, Wilma Olson, De Witt SumnersUpdated on Apr 17, 2007 04:59 AM PDT 
Lie groups and the method of the moving frame
Organizers: Robert Bryant and Jeanne N. ClellandUpdated on Apr 17, 2007 04:57 AM PDT 
Summer Graduate Workshop in Nonlinear dynamics of lowdimensional continua
Organizers: Anette Hosoi and L. MahadevanUpdated on Apr 17, 2007 04:57 AM PDT 
Cryptography
Organizers: Neal Koblitz, Alfred MenezesUpdated on Feb 12, 2007 09:47 AM PST 
Algebra, Algorithms, and Approximation
Organizers: Dave Bayer, Ilan Vardi, John StrainUpdated on Feb 12, 2007 09:45 AM PST 
Random Walk and Geometry
Organizers: Persi Diaconis, Laurent SaloffCosteUpdated on Feb 12, 2007 09:45 AM PST 
Hyperbolic Geometry
Organizers: William P. Thurston, Jane Gilman, David EpsteinUpdated on Feb 12, 2007 09:47 AM PST 
Automorphic Forms and Zeta Functions
Organizers: Dan Bump, Dinakar RamakrishnanUpdated on Feb 12, 2007 09:47 AM PST 
Mathematical Biology
Organizers: N. Kopell, C. Peskin, M. Reed (chairman), J. RinzelUpdated on Feb 23, 2007 08:45 AM PST 
4Manifolds
Organizers: Rob Kirby, Ron SternUpdated on May 17, 2007 06:46 AM PDT

Past Summer Graduate Schools 