
Summer Graduate School 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 Mar 23, 2016 09:35 AM PDT 
Summer Graduate School 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 Feb 11, 2016 02:10 PM PST
Past Educational Events

Summer Graduate School 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 
Summer Graduate School Mixed Integer Nonlinear Programming: Theory, algorithms and applications
Organizers: Franscisco Castro (University of Sevilla), Elena Fernandez (Universitat Politècnica 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 
Summer Graduate School 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 Jul 19, 2016 01:17 PM PDT 
MSRIUP MSRIUP 2016: Sandpile Groups
Organizers: Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Mercedes Franco (Queensborough Community College (CUNY)), Herbert Medina (Loyola Marymount University), LEAD Suzanne Weekes (Worcester Polytechnic Institute)The MSRIUP summer program is designed for undergraduate students who have completed two years of universitylevel mathematics courses and would like to conduct research in the mathematical sciences. Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply and the program cannot accept foreign students regardless of funding. The academic portion of the 2016 program will be led by Prof. Luis GarciaPuente of Sam Houston State University.
Updated on Jul 19, 2016 09:35 AM PDT 
Summer Graduate School 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 
Workshop Bay Area Discrete (BAD) Math Day 32
Organizers: Federico Ardila (San Francisco State University), Ralucca Gera (Naval Postgraduate School), Elizabeth Gross (San Jose State University), Angela Hicks (Stanford University), Carol Meyers (Lawrence Livermore National Laboratory), Rick Scott (University of Santa Clara), Erik Slivenken (University of California, Davis), Ellen Veomett (Saint Mary's College of California), Yan Zhang (University of California, Berkeley)Bay Area Discrete Math Days are oneday meetings aimed at facilitating communication between researchers and graduate students of discrete mathematics around the San Francisco Bay Area.These days happen semiannually and strive to create an informal atmosphere to talk about discrete mathematics. The term "discrete mathematics" is chosen to include at least the following topics: Algebraic and Enumerative Combinatorics, Discrete Geometry, Graph Theory, Coding and Design Theory, Combinatorial Aspects of Computational Algebra and Geometry, Combinatorial Optimization, Probabilistic Combinatorics, and Combinatorics in Mathematical Physics
Updated on Feb 19, 2016 03:13 PM PST 
Workshop Critical Issues in Mathematics Education 2016: Observing, Evaluating and Improving Mathematics Teaching from the Early Grades through the University
Organizers: Hyman Bass (University of Michigan), Michael Driskill (Math for America ), LEAD Mark Hoover (University of Michigan), LEAD Deborah Hughes Hallett (University of Arizona), Danny Martin (University of Illinois at Chicago), Miriam Sherin (Northwestern University)The 2016 CIME workshop focuses directly on the teaching of mathematics at the university and precollege levels. Teaching is not easy to examine in disciplined ways because it is so familiar and seems so obvious. Although teaching shapes students’ opportunities to learn, what teachers are actually doing is difficult to observe and describe. This impedes work on improving teaching.
This workshop will offer the opportunity to study and talk closely about mathematics teaching through close observation and discussion of video tapes in a setting that will bring together professionals with a range of perspectives, knowledge, experience, and orientations. The goal of the workshop is to develop language and methods for describing, analyzing and evaluating what can be seen in the classroom, with the ultimate goal of helping us shape and improve teaching — our own and more broadly.
Four questions structure the highly interactive design of the workshop: What skills are needed for observing teaching in ways that inform improvement efforts? What is involved in observing teaching? What is the teacher saying and doing? What are students saying and doing? What is the mathematics at play? What else is happening? And what do these imply for teaching?
 How can the practice and use of observation be structured in order to improve mathematics teaching? What approaches are available? What are their strengths and weaknesses?
 Observationbased assessment of teaching: Why, what, and how? What are the risks?
 How can we develop and sustain a crossprofessional community that observes and evaluates teaching in such a way that different communities communicate with and learn from each other to support a cycle of improvement in the teaching of mathematics at all levels?
The workshop will provide a library of videos of mathematics teaching for study. In addition, participants are encouraged to submit a short video clip of their own teaching, together with a brief background commentary. These videos will provide a central text for our collective work on discussing and assessing mathematics teaching.
Updated on Apr 08, 2016 11:41 AM PDT 
Workshop Modern Math Workshop 2015
Organizers: LEAD Hélène Barcelo (MSRI  Mathematical Sciences Research Institute), Helen Chamberlin (Ohio State University), Ricardo Cortez (Tulane University), Sujit Ghosh (NC State University), Dagan Karp (Harvey Mudd College), Anne Pfister (MSRI  Mathematical Sciences Research Institute), Christian Ratsch (University of California, Los Angeles), Ivelisse M. Rubio (University of Puerto Rico), Mariel Vazquez (University of California, Davis), Talithia Williams (Harvey Mudd College)As part of the Mathematical Sciences Collaborative Diversity Initiatives, nine mathematics institutes are pleased to host their annual SACNAS preconference event, the 2015 Modern Math Workshop (MMW). The Modern Math Workshop is intended to encourage minority undergraduates to pursue careers in the mathematical sciences and to assist undergraduates, graduate students and recent PhD’s in building their research networks.
Updated on Oct 12, 2015 11:12 AM PDT 
Summer Graduate School 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 
Summer Graduate School 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 Oct 21, 2015 12:36 PM PDT 
Summer Graduate School 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 
Summer Graduate School 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 
Summer Graduate School 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 
Summer Graduate School 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 
Summer Graduate School 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 
Summer Graduate School 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 
MSRIUP MSRIUP 2015: Geometric Combinatorics Motivated by the Social Sciences
Organizers: Federico Ardila (San Francisco State University), LEAD Duane Cooper (Morehouse College), Herbert Medina (Loyola Marymount University), Ivelisse M. Rubio (University of Puerto Rico), Suzanne Weekes (Worcester Polytechnic Institute)The MSRIUP summer program is designed for undergraduate students who have completed two years of universitylevel mathematics courses and would like to conduct research in the mathematical sciences. Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply and the program cannot accept foreign students regardless of funding. The academic portion of the 2015 program will be led by Prof. Francis Su from Harvey Mudd College.
Updated on Jul 27, 2015 01:57 PM PDT 
Workshop Partnerships: a Workshop on Collaborations between the NSF/MPS and Private Foundations
Organizers: Cynthia Atherton (HeisingSimons Foundation), Paulette Clancy (Cornell University), LEAD David Eisenbud (MSRI  Mathematical Sciences Research Institute), Thomas Everhart (California Institute of Technology), Caty Pilachowski (Indiana University, Bloomington), Robert Shelton (Research Corporation for Science Advancement), Yuri Tschinkel (New York University, Courant Institute)The National Science Foundation (NSF) and nonprofit organizations each provide critical support to the U.S. basic research enterprise in the mathematical and physical sciences. While the missions of these funders differ, many of their goals align and the grantee communities have significant overlap. With the ultimate aim of helping to advance the scientific frontier in the most effective way, we propose to hold a workshop to examine partnerships between the Directorate of Mathematical and Physical Sciences (MPS) at NSF and nonprofit funders in MPSrelated disciplines to
• understand different models of collaboration (the “how”);
• understand different motivations for collaboration (the “why”); and
• develop opportunities for future communication and/or collaboration.Updated on Jan 19, 2016 12:39 PM PST 
Workshop Critical Issues in Mathematics Education 2015: Developmental Mathematics: For whom? Toward what ends?
Organizers: Duane Cooper (Morehouse College), Mark Hoover (University of Michigan), LEAD Robert Megginson (University of Michigan), Richard Sgarlotti (Bay College), Katherine Stevenson (California State University, Northridge)This workshop will address the critical issue of developmental mathematics at two and fouryear colleges and universities and the broader dynamic of mathematics remediation that occurs at all levels. It will engage mathematicians, K12 teachers, mathematics educators, and administrators in a conversation about the goals of developmental mathematics and the contributions that our different professional communities make to this work. Key questions that will be addressed are:
1. How do we teach content in ways that acknowledge and leverage each student's prior learning experiences? In particular, how do we take advantage of a student's maturity while refining his or her learning habits where necessary?
2. How can developmental mathematics instruction move students through mathematics which must be relearned while simultaneously gaining momentum on more advanced mathematics (including the development of mathematical practices needed for meaningful mathematical work)?
3. What are strategies for supporting the needs of the wide range of students in developmental mathematics programsthose developing mathematical skills for life in general as well as those developing the foundation necessary to proceed towards a STEM major? How can we successfully address equity issues raised for students from groups underrepresented in STEM fields? How can developmental mathematics instruction blend synchronous and asynchronous instruction to achieve maximal efficiency and impact?
4. What is the proper balance between addressing the needs of the wide range of students mentioned in the preceding point and keeping instruction and course offerings concise?
5. What are the characteristics, training, and practices of a successful developmental mathematics teacher?
6. What support services enhance the success of a developmental mathematics program?
Updated on Apr 01, 2015 03:27 PM PDT 
Summer Graduate School 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 11, 2014 12:16 PM PDT 
Summer Graduate School 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 Jun 24, 2014 02:31 PM PDT 
Summer Graduate School 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 
Summer Graduate School 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 
Summer Graduate School 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 
MSRIUP MSRIUP 2014: Arithmetic Aspects of Elementary Functions
Organizers: Duane Cooper (Morehouse College), Ricardo Cortez (Tulane University), LEAD Herbert Medina (Loyola Marymount University), Ivelisse M. Rubio (University of Puerto Rico), Suzanne Weekes (Worcester Polytechnic Institute)The MSRIUP summer program is designed for undergraduate students who have completed two years of universitylevel mathematics courses and would like to conduct research in the mathematical sciences. Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply and the program cannot accept foreign students regardless of funding. The academic portion of the 2014 program will be led by Dr. Victor Moll from Tulane University.
Updated on Apr 02, 2015 01:15 PM PDT 
Summer Graduate School 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