# Mathematical Sciences Research Institute

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1. # Toric Varieties (National Center for Theoretical Sciences, Taipei)

Organizers: David Cox (Amherst College), Henry Schenck (Auburn University)
This simplicial fan in 3-dimensional space

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 Aug 08, 2019 09:27 AM PDT
2. # Mathematics of Machine Learning

Organizers: Sebastien Bubeck (Microsoft Research), Anna Karlin (University of Washington), Adith Swaminathan (Microsoft Research)
Popular visualization of the MNIST dataset

Learning theory is a rich field at the intersection of statistics, probability, computer science, and optimization. Over the last decades the statistical learning approach has been successfully applied to many problems of great interest, such as bioinformatics, computer vision, speech processing, robotics, and information retrieval. These impressive successes relied crucially on the mathematical foundation of statistical learning.

Recently, deep neural networks have demonstrated stunning empirical results across many applications like vision, natural language processing, and reinforcement learning. The field is now booming with new mathematical problems, and in particular, the challenge of providing theoretical foundations for deep learning techniques is still largely open. On the other hand, learning theory already has a rich history, with many beautiful connections to various areas of mathematics (e.g., probability theory, high dimensional geometry, game theory). The purpose of the summer school is to introduce graduate students (and advanced undergraduates) to these foundational results, as well as to expose them to the new and exciting modern challenges that arise in deep learning and reinforcement learning.

Updated on Aug 01, 2019 10:00 AM PDT
3. # H-Principle (INdAM, Cortona, Italy)

Organizers: LEAD Emmy Murphy (Northwestern University), Takashi Tsuboi (University of Tokyo)
The image of a large sphere isometrically embedded into a small space through a C^1 embedding. (Attributions: E. Bartzos, V. Borrelli, R. Denis, F. Lazarus, D. Rohmer, B. Thibert)

This two week summer school will introduce graduate students to the theory of h-principles.  After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, fluid dynamics, and foliation theory.

Updated on Aug 08, 2019 09:31 AM PDT
4. # Recent topics on well-posedness and stability of incompressible fluid and related topics

Organizers: LEAD Yoshikazu Giga (University of Tokyo), Maria Schonbek (University of California, Santa Cruz), Tsuyoshi Yoneda (University of Tokyo)
Fluid-flow stream function color-coded by vorticity in 3D flat torus calculated by K. Nakai (The University of Tokyo)

The purpose of the workshop is to introduce graduate students to fundamental results on the Navier-Stokes and the Euler equations, with special emphasis on the solvability of its initial value problem with rough initial data as well as the large time behavior of a solution. These topics have long research history. However, recent studies clarify the problems from a broad point of view, not only from analysis but also from detailed studies of orbit of the flow.

Updated on Aug 19, 2019 04:17 PM PDT
5. # Polynomial Method

Organizers: Adam Sheffer (Bernard M. Baruch College, CUNY), LEAD Joshua Zahl (University of British Columbia)
from distinct distances in the plane to line incidences in R^3

In the past eight years, a number of longstanding open problems in combinatorics were resolved using a new set of algebraic techniques. In this summer school, we will discuss these new techniques as well as some exciting recent developments.

Updated on Jul 12, 2019 03:36 PM PDT
6. # Séminaire de Mathématiques Supérieures 2019: Current trends in Symplectic Topology

Organizers: Octav Cornea (Université de Montréal), Yakov Eliashberg (Stanford University), Michael Hutchings (University of California, Berkeley), Egor Shelukhin (Université de Montréal)
A Holomorphic Curve

Symplectic topology is a fast developing branch of geometry that has seen phenomenal growth in the last twenty years. This two weeks long summer school, organized in the setting of the Séminaire de Mathématiques Supérieures, intends to survey some of the key directions of development in the subject today thus covering: advances in homological mirror symmetry; applications to hamiltonian dynamics; persistent homology phenomena; implications of flexibility and the dichotomy flexibility/rigidity; legendrian contact homology; embedded contact homology and four-dimensional holomorphic techniques and others. With the collaboration of many of the top researchers in the field today, the school intends to serve as an introduction and guideline to students and young researchers who are interested in accessing this diverse subject.

Updated on Dec 10, 2018 04:21 PM PST
7. # Geometric Group Theory

Organizers: LEAD Rita Jiménez Rolland (Instituto de Matematicás, UNAM-Oaxaca), LEAD Pierre Py (Universidad Nacional Autónoma de México)
Rips's δ-thin triangle condition for Gromov hyperbolicity of metric spaces (Stomatapoll)

Geometric group theory studies discrete groups by understanding the connections between algebraic properties of these groups and topological and geometric properties of the spaces on which they act. The aim of this summer school is to  introduce graduate students to specific central topics and recent developments in geometric group theory. The school will also include students presentations to give the participants an opportunity to practice their speaking skills in mathematics.  Finally, we hope that this meeting will help connect Latin American students with their American and Canadian counterparts in an environment that encourages discussion and collaboration.

Updated on Jul 03, 2019 11:35 AM PDT
8. # Representation stability

Organizers: Thomas Church (Stanford University), LEAD Andrew Snowden (University of Michigan), Jenny Wilson (University of Michigan)
An illustration of an adaptation of Quillen's classical homological stability spectral sequence argument

This summer school will give an introduction to representation stability, the study of algebraic structural properties and stability phenomena exhibited by sequences of representations of finite or classical groups -- including sequences arising in connection to hyperplane arrangements, configuration spaces, mapping class groups, arithmetic groups, classical representation theory, Deligne categories, and twisted commutative algebras.  Representation stability incorporates tools from commutative algebra, category theory, representation theory, algebraic combinatorics, algebraic geometry, and algebraic topology. This workshop will assume minimal prerequisites, and students in varied disciplines are encouraged to apply.

Updated on Jul 03, 2019 03:47 PM PDT
9. # Random and arithmetic structures in topology

Organizers: LEAD Alexander Furman (University of Illinois at Chicago), Yizhaq Gelander (Weizmann Institute of Science)

The study of locally symmetric manifolds, such as closed hyperbolic manifolds, involves geometry of the corresponding symmetric space, topology of towers of its finite covers, and number-theoretic aspects that are relevant to possible constructions.
The workshop will provide an introduction to these and closely related topics such as lattices, invariant random subgroups, and homological methods.

Updated on Jul 09, 2019 08:17 AM PDT
10. # Commutative Algebra and its Interaction with Algebraic Geometry

Organizers: Craig Huneke (University of Virginia), Sonja Mapes (University of Notre Dame), Juan Migliore (University of Notre Dame), LEAD Claudia Polini (University of Notre Dame), Claudiu Raicu (University of Notre Dame)
The figure represents a blow-up. The so called blow-up algebras or Rees rings are the algebraic realizations of such blow-ups.

Linkage is a method for classifying ideals in local rings. Residual intersections is a generalization of linkage to the case where the two linked' ideals  need not have the same codimension. Residual intersections are ubiquitous: they play an important role in the study of blowups, branch and multiple point loci, secant varieties, and Gauss images; they appear naturally in intersection theory; and they have close connections with integral closures of ideals.

Commutative algebraists have long used the Frobenius or p-th power map to study commutative rings containing a finite fi eld. The theory of tight closure and test ideals has widespread applications to the study of symbolic powers and to Briancon-Skoda type theorems for equi-characteristic rings.

Numerical conditions for the integral dependence of ideals and modules have a wealth of applications, not the least of which is in equisingularity theory. There is a long history of generalized criteria for integral dependence of ideals and modules based on variants of the Hilbert-Samuel and the Buchsbaum-Rim multiplicity that still require some remnants of finite length assumptions.

The Rees ring and the special fiber ring of an ideal arise in the process of blowing up a variety along a subvariety. Rees rings and special fiber rings also describe, respectively, the graphs and the images of rational maps between projective spaces. A difficult open problem in commutative algebra, algebraic geometry, elimination theory, and geometric modeling is to determine explicitly the equations defining graphs and images of rational maps.

The school will consist of the following four courses with exercise sessions plus a Macaulay2 workshop

• Characteristic p methods and applications
• Blowup algebras
• Multiplicity theory

Updated on May 29, 2019 09:11 AM PDT
11. # From Symplectic Geometry to Chaos

Organizers: Marcel Guardia (Polytechnical University of Cataluña (Barcelona) ), vadim kaloshin (University of Maryland), Leonid Polterovich (Tel Aviv University)

The purpose of the summer school is to introduce graduate students to state-of-the-art methods and results in Hamiltonian systems and symplectic geometry. We focus on recent developments on the study of chaotic motion in Hamiltonian systems and its applications to models in Celestial Mechanics.

Updated on Jul 31, 2018 12:12 PM PDT
12. # Representations of High Dimensional Data

Organizers: Blake Hunter (Microsoft), Deanna Needell (University of California, Los Angeles)

In today's world, data is exploding at a faster rate than computer architectures can handle. This summer school will introduce students to modern and innovative mathematical techniques that address this phenomenon. Hands-on topics will include data mining, compression, classification, topic modeling, large-scale stochastic optimization, and more.

Updated on Jul 19, 2018 11:45 AM PDT
13. # IAS/PCMI 2018: Harmonic Analysis

Organizers: Carlos Kenig (University of Chicago), Fanghua Lin (New York University, Courant Institute), Svitlana Mayboroda (University of Minnesota, Twin Cities), Tatiana Toro (University of Washington)

Harmonic analysis is a central field of mathematics with a number of applications to geometry, partial differential equations, probability, and number theory, as well as physics, biology, and engineering. The Graduate Summer School will feature mini-courses in geometric measure theory, homogenization, localization, free boundary problems, and partial differential equations as they apply to questions in or draw techniques from harmonic analysis. The goal of the program is to bring together students and researchers at all levels interested in these areas to share exciting recent developments in these subjects, stimulate further interactions, and inspire the new generation to pursue research in harmonic analysis and its applications.

Updated on Jun 20, 2018 12:17 PM PDT
14. # Derived Categories

Organizers: Nicolas Addington (University of Oregon), LEAD Alexander Polishchuk (University of Oregon)

The goal of the school is to give an introduction to basic techniques for working with derived categories, with an emphasis on the derived categories of coherent sheaves on algebraic varieties. A particular goal will be to understand Orlov’s equivalence relating the derived category of a projective hypersurface with matrix factorizations of the corresponding polynomial.

Updated on Jul 05, 2018 09:05 AM PDT
15. # H-principle

Organizers: Emmy Murphy (Northwestern University), Takashi Tsuboi (University of Tokyo)
The image of a large sphere isometrically embedded into a small space through a C^1 embedding. (Attributions: E. Bartzos, V. Borrelli, R. Denis, F. Lazarus, D. Rohmer, B. Thibert)

This two week summer school will introduce graduate students to the theory of h-principles.  After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, and foliation theory.

Updated on Jun 20, 2018 12:17 PM PDT
16. # Mathematical Analysis of Behavior

Organizers: Ann Hermundstad (Janelia Research Campus, HHMI), Vivek Jayaraman (Janelia Research Campus, HHMI), Eva Kanso (University of Southern California), L. Mahadevan (Harvard University)

Explore Outstanding Phenomena in Animal Behavior

Jointly hosted by Janelia and the Mathematical Sciences Research Institute (MSRI), this program will bring together 15-20 advanced PhD students with complementary expertise who are interested in working at the interface of mathematics and biology. Emphasis will be placed on linking behavior to neural dynamics and exploring the coupling between these processes and the natural sensory environment of the organism. The aim is to educate a new type of global scientist that will work collaboratively in tackling complex problems in cellular, circuit and behavioral biology by combining experimental and computational techniques with rigorous mathematics and physics.

Updated on Jun 20, 2018 12:16 PM PDT
17. # The ∂-Problem in the Twenty-First Century

Organizers: Debraj Chakrabarti (Central Michigan University), Jeffery McNeal (Ohio State University)

This Summer Graduate School will introduce students to the modern theory of the  inhomogeneous Cauchy-Riemann equation, the fundamental partial differential equation of Complex Analysis. This theory uses powerful tools of partial differential equations, differential geometry and functional analysis to obtain a refined understanding of holomorphic functions on complex manifolds. Besides students planning to work in complex analysis, this course will be valuable to those planning to study partial differential equations, complex differential and algebraic geometry, and operator theory. The exposition will be self-contained and the prerequisites will be kept at a minimum

Updated on Jun 21, 2018 01:13 PM PDT
18. # Séminaire de Mathématiques Supérieures 2018: Derived Geometry and Higher Categorical Structures in Geometry and Physics

Organizers: Anton Alekseev (Université de Genève), Ruxandra Moraru (University of Waterloo), Chenchang Zhu (Universität Göttingen)

Higher categorical structures and homotopy methods have made significant influence on geometry in recent years. This summer school is aimed at transferring these ideas and fundamental technical tools to the next generation of mathematicians.

The summer school will focus on the following four topics:  higher categorical structures in geometry, derived geometry, factorization algebras, and their application in physics.  There will be eight to ten mini courses on these topics, including mini courses led by Chirs Brav, Kevin Costello, Jacob Lurie, and Ezra Getzler. The prerequisites will be kept at a minimum, however, a introductory courses in differential geometry, algebraic topology and abstract algebra are recommended.

Updated on Jun 20, 2018 12:16 PM PDT
19. # Automorphic Forms and the Langlands Program

Organizers: LEAD Kevin Buzzard (Imperial College, London)

The summer school will be an introduction to the more algebraic aspects of the theory of automorphic forms and representations. One of the goals will be to understand the statements of the main conjectures in the Langlands programme. Another will be to gain a good working understanding of the fundamental definitions in the theory, such as principal series representations, the Satake isomorphism, and of course automorphic forms and representations for groups such as GL_n and its inner forms.

Updated on Aug 04, 2017 11:02 AM PDT
20. # Nonlinear dispersive PDE, quantum many particle systems and the world between

Organizers: Natasa Pavlovic (University of Texas, Austin), Gigliola Staffilani (Massachusetts Institute of Technology), Nikolaos Tzirakis (University of Illinois at Urbana-Champaign)

The purpose of the summer school is to introduce graduate students to the recent developments in the area of dispersive partial differential equations (PDE), which have received a great deal of attention from mathematicians, in part due to ubiquitous applications to nonlinear optics, water wave theory and plasma physics.

Recently remarkable progress has been made in understanding existence and uniqueness of solutions to nonlinear Schrodinger (NLS) and KdV equations, and properties of those solutions. We will outline the basic tools that were developed to address these questions. Also we will present some of recent results on derivation of NLS equations from quantum many particle systems and will discuss how methods developed to study the NLS can be relevant in the context of the derivation of this nonlinear equation.

Updated on Sep 12, 2017 02:02 PM PDT
21. # Séminaire de Mathématiques Supérieures 2017: Contemporary Dynamical Systems

Organizers: Sylvain Crovisier (Université de Paris VI (Pierre et Marie Curie)-Université de Paris XI (Paris-Sud)), LEAD Konstantin Khanin (University of Toronto), Andrés Navas Flores (University of Santiago de Chile), Christiane Rousseau (Université de Montréal), Marcelo Viana (Institute of Pure and Applied Mathematics (IMPA)), Amie Wilkinson (University of Chicago)

The theory of dynamical systems has witnessed very significant developments in the last decades, includi​n​g the work of two 2014 Fields medalists, Artur Avila and Maryam Mirzakhani. ​The school will concentrate on the recent significant developments in the field of dynamical systems and present some of the present main streams of research. Two central themes will be those of partial hyperbolicity on one side, and rigidity, group actions and renormalization on the other side.​ ​Other themes will ​include homogeneous dynamics and geometry and dynamics on infinitely flat surfaces (both providing connections to the work of Maryam Mirzakhani), topological dynamics, thermodynamical formalism, singularities and bifurcations in analytic dynamical systems.

Updated on May 06, 2017 01:18 AM PDT
22. # Positivity Questions in Geometric Combinatorics

Organizers: Eran Nevo (The Hebrew University of Jerusalem), Raman Sanyal (Johann Wolfgang Goethe-Universität Frankfurt)

McMullen’s g-Conjecture from 1970 is a shining example of mathematical foresight that combined all results available at that time to conjure a complete characterization of face numbers of convex simple/simplicial polytopes. The key statement in its verification is that certain combinatorial numbers associated to geometric (or topological) objects are non-negative. The aim of this workshop is to introduce graduate students to selected contemporary topics in geometric combinatorics with an emphasis on positivity questions. It is fascinating that the dual notions of simple and simplicial polytopes lead to different but equally powerful algebraic frameworks to treat such questions. A key feature of the lectures will be the simultaneous development of these algebraic frameworks from complementary perspectives: combinatorial-topological and convex-geometric.  General concepts (such as Lefschetz elements, Hodge–Riemann–Minkowski inequalities) will be developed side-by-side, and analogies will be drawn to concepts in algebraic geometry, Fourier analysis, rigidity theory and measure theory. This allows for entry points for students with varying backgrounds.  The courses will be supplemented with guest lectures highlighting further connections to other fields.

Updated on Jul 21, 2017 10:13 AM PDT
23. # Soergel Bimodules

Organizers: LEAD Ben Elias (University of Oregon), Geordie Williamson (University of Sydney)

We will give an introduction to categorical representation theory, focusing on the example of Soergel bimodules, which is a categorification of the Iwahori-Hecke algebra. We will give a comprehensive introduction to the "tool box" of modern (higher) representation theory: diagrammatics, homotopy categories, categorical diagonalization, module categories, Drinfeld center, algebraic Hodge theory.

Updated on Jul 10, 2017 01:18 PM PDT
24. # Subfactors: planar algebras, quantum symmetries, and random matrices

Organizers: LEAD Scott Morrison (Australian National University), Emily Peters (Loyola University), Noah Snyder (Indiana University)

Subfactor theory is a subject from operator algebras, with many surprising connections to other areas of mathematics. This summer school will be devoted to understanding the representation theory of subfactors, with a particular emphasis on connections to quantum symmetries, fusion categories, planar algebras, and random matrices

Updated on Jun 20, 2017 03:34 PM PDT
25. # Commutative Algebra and Related Topics

Organizers: Shinobu Hikami (Okinawa Institute of Science and Technology), LEAD Shihoko Ishii (Tsinghua University), Kazuhiko Kurano (Meiji University), Ken-ichi Yoshida (Nihon University)

The purpose of the school will be to introduce graduate students to foundational results in commutative algebra, with particular emphasis of the diversity of the related topics with commutative algebra. Some of these topics are developing remarkably in this decade and through learning those subjects the graduate students will be stimulated toward future research.

Updated on Jun 21, 2017 04:53 PM PDT
26. # Chip Firing and Tropical Curves

Organizers: LEAD Matthew Baker (Georgia Institute of Technology), David Jensen (University of Kentucky), Sam Payne (University of Texas, Austin)

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 May 06, 2017 01:18 AM PDT
27. # 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 Kohn-Sham density functional theory (KS-DFT), 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 self-contained introduction to electronic structure theory, with particular emphasis on frontier topics in aspects of applied analysis and numerical methods.

Updated on May 06, 2017 01:18 AM PDT
28. # An Introduction to Character Theory and the McKay Conjecture

Organizers: Robert Guralnick (University of Southern California), Pham Tiep (Rutgers University)

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.

Group Photo

Updated on May 06, 2017 01:18 AM PDT
29. # Mixed Integer Nonlinear Programming: Theory, algorithms and applications

Organizers: Francisco Castro (University of Sevilla), Elena Fernandez (Polytechnical University of Cataluña (Barcelona) ), 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 non-specialist, 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 06, 2017 01:18 AM PDT
30. # 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.

Group Photo

Updated on May 06, 2017 01:18 AM PDT
31. # 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 bio-networks, multi scale biological dynamics, biological waves, nonlinear dynamics of pattern formation, and disease dynamics. For each of the five key areas, we will invite 2-3 world leaders who are also excellent communicators to deliver a series of 2-4 one-hour lectures. We expect an average of eight hours of lecture per subject area, spread over approximately two weeks.

Updated on May 06, 2017 01:18 AM PDT
32. # Incompressible Fluid Flows at High Reynolds Number

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 May 06, 2017 01:18 AM PDT
33. # Gaps between Primes and Analytic Number Theory

Organizers: Dimitris Koukoulopoulos (Université de Montréal), LEAD Emmanuel Kowalski (ETH Zurich), 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 May 06, 2017 01:18 AM PDT
34. # 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 state-of–the-art 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 May 06, 2017 01:18 AM PDT
35. # 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 May 06, 2017 01:18 AM PDT
36. # 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 May 06, 2017 01:18 AM PDT
37. # 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 May 06, 2017 01:18 AM PDT
38. # 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 May 06, 2017 01:18 AM PDT
39. # CRM-PIMS Summer School in Probability

Organizers: LEAD Louigi Addario-Berry (McGill University), Louis-Pierre Arguin (University of Montreal), Alexander Fribergh (University of Montreal), 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 May 06, 2017 01:18 AM PDT
40. # Geometry and Analysis

Organizers: Hans-Joachim 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, Kahler-Einstein manifolds, and the analysis of Riemann surfaces.

Updated on May 06, 2017 01:18 AM PDT
41. # 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 May 01, 2019 02:31 PM PDT
42. # Algebraic Topology

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

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 May 06, 2017 01:18 AM PDT
43. # 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 May 06, 2017 01:18 AM PDT
44. # Seminaire de Mathematiques Superieures 2014: Counting Arithmetic Objects

Organizers: Henri Darmon (McGill University), Andrew Granville (Université de Montréal), Benedict Gross (Harvard University)

Updated on May 06, 2017 01:18 AM PDT
45. # Dispersive Partial Differential Equations

Organizers: Natasa Pavlovic (University of Texas, Austin), 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 May 01, 2019 02:26 PM PDT
46. # 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 Aug 16, 2019 01:33 PM PDT
47. # 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 May 06, 2017 01:18 AM PDT
48. # New Geometric Techniques in Number Theory

Organizers: Toby Gee (Imperial College, London), LEAD Ariane Mézard (Institut de Mathématiques de Jussieu; École Normale Supérieure), 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 May 01, 2019 01:19 PM PDT
49. # 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.

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, 2017 01:18 AM PDT
50. # 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)

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, 2017 01:18 AM PDT
51. # Algebraic Topology

Organizers: Andrew Blumberg (University of Texas, Austin), Teena Gerhardt (Michigan State University), LEAD Michael Hill (University of California, Los Angeles)

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 May 06, 2017 01:18 AM PDT
52. # 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 Apr 19, 2020 12:20 AM PDT
53. # 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 Jul 02, 2020 12:20 AM PDT
54. # 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
55. # Seminaire de Mathematiques Superieures 2012: Probabilistic Combinatorics

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

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
56. # 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 Jun 30, 2020 12:20 AM PDT
57. # 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 Jun 17, 2020 12:20 AM PDT
58. # 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
59. # 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 Jun 27, 2020 12:20 AM PDT
60. # 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
61. # 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 Mar 24, 2020 09:49 AM PDT
62. # 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 Mar 30, 2020 12:20 AM PDT
63. # 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 Jul 01, 2020 12:20 AM PDT
64. # 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 Jul 02, 2020 01:33 PM PDT
65. # 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.

Updated on Jul 05, 2018 10:46 AM PDT
66. # 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 Jun 16, 2020 02:05 PM PDT
67. # 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.

Updated on Apr 21, 2020 09:41 AM PDT
68. # 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 Jun 29, 2020 12:20 AM PDT
69. # 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 Jul 12, 2019 03:29 PM PDT
70. # 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 Jul 05, 2020 12:20 AM PDT
71. # 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 Jul 04, 2020 12:20 AM PDT
72. # 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
73. # 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 Jul 03, 2020 12:20 AM PDT
74. # IAS/PCMI Summer Program: The Arithmetic of L-functions

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
75. # 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 Jul 01, 2020 12:20 AM PDT
76. # 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 Mar 23, 2020 02:11 PM PDT
77. # 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 Jun 23, 2020 12:20 AM PDT
78. # IAS/PCMI Summer Program: Analytic and Algebraic Geometry: Common Problems - Different Methods

Organizers: Mircea Mustaţă (University of Michigan), Jeff McNeal (Ohio State University)

Updated on May 08, 2019 11:51 AM PDT
79. # 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 Jun 04, 2020 12:20 AM PDT
80. # 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 Jul 05, 2020 12:20 AM PDT
81. # Continuous Optimization and Applications

Organizers: Henry Wolkowicz. (University of Waterloo)

Updated on Jun 10, 2020 12:20 AM PDT
82. # Summer Graduate Workshop on Data Assimilation for the Carbon Cycle

Updated on Dec 01, 2008 02:26 AM PST
83. # IAS/PCMI summer conference: Statistical Mechanics

Organizers: Scott Sheffield, Thomas Spencer

Updated on Dec 01, 2008 02:24 AM PST
84. # 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 May 15, 2020 03:50 PM PDT
85. # 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 May 03, 2020 12:20 AM PDT
86. # 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 Dec 29, 2019 12:20 AM PST
87. # 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 Jul 05, 2020 12:20 AM PDT
88. # 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 Jul 03, 2020 12:20 AM PDT
89. # 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 Jan 02, 2020 02:59 PM PST
90. # Computing the Continuous Discretely: Integer Point Enumeration in Polyhedra (Summer Graduate Workshop)

Organizers: Mathias Beck and Sinai Robins

Updated on Feb 12, 2007 09:39 AM PST
91. # CR Geometry: Complex Analysis Meets Real Geometry and Number Theory

Organizers: John D’Angelo

Updated on Mar 28, 2020 12:20 AM PDT
92. # AMS-IMS-SIAM Summer School in Commutative Algebra: Local Cohomology and Its Applications

Organizers: Anurag Singh and Uli Walther

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

Updated on Dec 01, 2008 06:01 AM PST
93. # 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 Rossi

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

Updated on Jul 04, 2020 12:20 AM PDT
94. # Mathematical Graphics

Organizers: David Austin, Bill Casselman and Jim Fix

Updated on Dec 01, 2008 06:02 AM PST
95. # 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
96. # Knot Theory and 3-Manifolds (Summer Graduate Workshop)

Organizers: S. Boyer (UQAM), R. Fenn (Sussex), D. Rolfsen, Chair (UBC), D. Sjerve (UBC)

Updated on May 23, 2018 03:22 PM PDT
97. # 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
98. # Triangulations of Point Sets: Applications, Structures, Algorithms

Organizers: Jesús A. De Loera, Jörg Rambau, and Francisco Santos

Updated on May 13, 2013 11:00 PM PDT
99. # Mathematical Graphics

Organizers: Bill Casselman and David Austin

Updated on Feb 12, 2007 09:47 AM PST
100. # 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

Updated on Nov 18, 2019 12:20 AM PST
101. # 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
102. # Combinatorial Game Theory (Summer Graduate Workshop II)

Organizers: Elwyn Berlekamp and David Wolfe

Updated on Feb 07, 2007 06:04 AM PST
103. # MSRI/PMMB Short Course: Mathematical and Computational Challenges in Molecular and Cell Biology

Organizers: Nicholas R. Cozzarelli, Michael Levitt, Wilma Olson, De Witt Sumners

Updated on Jun 08, 2020 12:20 AM PDT
104. # Lie groups and the method of the moving frame

Organizers: Robert Bryant and Jeanne N. Clelland

Updated on Jun 28, 2020 12:20 AM PDT
105. # Lie groups and the method of the moving frame / Exterior Differential Systems

Organizers: Jeanne N. Clelland and Robert Bryant,

Updated on Oct 12, 2018 02:29 PM PDT
106. # Summer Graduate Workshop in Nonlinear dynamics of low-dimensional continua

Organizers: Anette Hosoi and L. Mahadevan

Updated on Mar 31, 2020 12:20 AM PDT
107. # Algorithmic Algebra and Geometry

Organizers: David Bayer, Sorin Popescu

Updated on Oct 12, 2018 02:38 PM PDT
108. # Cryptography

Organizers: Neal Koblitz, Alfred Menezes

Updated on Feb 12, 2007 09:47 AM PST
109. # Algebra, Algorithms, and Approximation

Organizers: Dave Bayer, Ilan Vardi, John Strain

Updated on Feb 12, 2007 09:45 AM PST
110. # Random Walk and Geometry

Organizers: Persi Diaconis, Laurent Saloff-Coste

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

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

Updated on Feb 12, 2007 09:47 AM PST
112. # Automorphic Forms and Zeta Functions

Organizers: Dan Bump, Dinakar Ramakrishnan

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

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

Updated on Feb 20, 2019 01:12 PM PST
114. # 4-Manifolds

Organizers: Rob Kirby, Ron Stern

Updated on May 17, 2007 06:46 AM PDT
115. # Computing the Continuous Discretely: Integer Point Enumeration in Polyhedra (Summer Graduate Program)

Organizers: Mathias Beck and Sinai Robins

Updated on Oct 25, 2016 10:05 AM PDT
116. # CR Geometry: Complex Analysis Meets Real Geometry and Number Theory

Organizers: John D’Angelo

Updated on Oct 25, 2016 10:06 AM PDT
117. # 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 Rossi

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

Updated on Oct 25, 2016 10:06 AM PDT
118. # Mathematical Graphics (Summer Graduate Program)

Organizers: David Austin, Bill Casselman and Jim Fix

Updated on Oct 25, 2016 10:06 AM PDT
119. # AMS-IMS-SIAM Summer School in Commutative Algebra: Local Cohomology and Its Applications

Organizers: Anurag Singh and Uli Walther

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

Updated on Oct 25, 2016 10:04 AM PDT
120. # 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 Oct 25, 2016 10:05 AM PDT
121. # Summer Graduate Program in Hyperplane Arrangements and Applications (Summer Graduate Program)

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 Oct 25, 2016 09:57 AM PDT
122. # SGP: Knot Theory and 3-Manifolds

Organizers: Steven Boyer, Roger A Fenn and Dale Rolfsen

Updated on Oct 25, 2016 09:57 AM PDT
123. # SGP: Analysis of Algorithms

Organizers: P. Flajolet, G. Seroussi, W. Szpankowski, and M. Weinberger

Updated on Oct 25, 2016 09:57 AM PDT
124. # SGP: Triangulations of Point Sets: Applications, Structures, Algorithms

Organizers: Jesús A. De Loera, Jörg Rambau, and Francisco Santos

Updated on Oct 25, 2016 09:57 AM PDT
125. # SGP: Mathematical Graphics

Organizers: Bill Casselman and David Austin

Updated on Oct 25, 2016 09:56 AM PDT
126. # SGP: 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

Updated on Oct 25, 2016 09:56 AM PDT
127. # SGP: 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 Oct 25, 2016 09:55 AM PDT
128. # SGP: The Global Theory of Minimal Surfaces

Organizers: Joel Hass and David Hoffman

MSRI's second Graduate Summer Program for 2001.

Updated on Oct 25, 2016 09:55 AM PDT
129. # SGP: Modern Signal Processing

Organizers: Dan Rockmore and Dennis Healy

MSRI's Summer Graduate Program I This summer graduate program, organized by Dan Rockmore and Dennis Healy, Jr., will introduce students to the world of signal processing. The course will cover standard tools of digital signal processing, but will also cover the exciting frontiers of the subject, including wavelets, ISP (integrated sensing and processing), image processing algorithms, etc. In addition, students will be briefly exposed to applications in various areas, such as biology, chemistry, medicine, music, and engineering.

Updated on Oct 25, 2016 09:55 AM PDT
130. # SGP: Combinatorial Game Theory

Organizers: E. Berlekamp, D. Wolfe

Updated on Oct 25, 2016 09:54 AM PDT
131. # SGP: Mathematical and Computational Challenges In Molecular and Cell Biology

Organizers: Nicholas R. Cozzarelli, Michael Levitt, Wilma Olson, De Witt Sumners

Updated on Oct 25, 2016 09:54 AM PDT
132. # SGP: Lie groups and the method of the moving frame / Exterior Differential Systems

Organizers: Jeanne N. Clelland and Robert Bryant,

Updated on Oct 25, 2016 09:54 AM PDT
133. # SGP: Nonlinear dynamics of low-dimensional continua

Organizers: L. Mahadevan and Anette Hosoi

Updated on Oct 25, 2016 09:53 AM PDT
134. # SGP: Algorithmic Algebra and Geometry

Organizers: David Bayer, Sorin Popescu

Updated on Oct 25, 2016 09:53 AM PDT
135. # SGP: Cryptography

Organizers: Neal Koblitz, Alfred Menezes

Updated on Oct 25, 2016 09:53 AM PDT
136. # SGP: Algebra, Algorithms, and Approximation

Organizers: Dave Bayer, Ilan Vardi, John Strain

Updated on Oct 25, 2016 09:52 AM PDT
137. # SGP: Random Walk and Geometry

Organizers: Persi Diaconis, Laurent Saloff-Coste

Updated on Oct 25, 2016 09:52 AM PDT
138. # SGP: Hyperbolic Geometry

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

Updated on Oct 25, 2016 09:51 AM PDT
139. # SGP: Automorphic Forms and Zeta Functions

Organizers: Dan Bump, Dinakar Ramakrishnan

Updated on Oct 25, 2016 09:49 AM PDT
140. # SGP: Mathematical Biology

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

Updated on Oct 25, 2016 09:48 AM PDT
141. # SGP: 4-Manifolds

Organizers: Rob Kirby, Ron Stern

Updated on Oct 25, 2016 09:32 AM PDT