View all upcoming workshops at MSRI.
Programmatic Workshops: Workshops related to MSRI's Scientific Programs fall into one of the following three categories.
Introductory workshops set the stage and provide the context for the scientific program, with the intended audience being researchers not in the program. This would include members in the other programs, members of the local mathematical community, and participants from outside the area selected especially for the workshop, particularly from groups underrepresented in research intensive contexts: women, minorities, mathematicians not located at research centers, and graduate students. In selecting participants, priority is given to these latter groups. Introductory Workshops have been effective in broadcasting the goals, ideas and techniques of a particular program to the mathematical public at large, as well as in bringing the MSRI community together as a whole.
Connections for Women Workshops
These two-day workshops are held immediately preceding the week of the Introductory Workshop. While different programs have approached these workshops in diverse ways, one of the principal objectives, strongly supported by MSRI's advisory committees, is to provide an enhanced opportunity for women researchers to interact with other women with similar research interests. MSRI's workshop organizers work together so that as many participating researchers as possible are supported to stay on for the Introductory Workshop. As is the case for all MSRI workshops, registration to attend Connections workshop lectures is open to all interested persons, not limited to women.
Directed toward the mathematical community at large, topical workshops are designed to interest and attract young researchers and other mathematicians active in the field. MSRI provides a yearly Hot Topics Workshop, to showcase what is new, innovative and interesting to the mathematical sciences community at the present time. The Critical Issues in Mathematics Education (CIME) workshop series offers an annual spring workshop designed to engage mathematicians, mathematics education researchers, and K-12 teachers to learn about research and development efforts that can enhance their own work and about the contributions they can make to solving the challenges of mathematics education.
Resources for Workshop Attendees
Mother's Room: MSRI is pleased to be able to offer a private room for nursing mothers.
Childcare Grants for Workshop Participants: As part of our dedication to supporting participation from all researchers in mathematics, we are excited to have generous donations from private funders to support child care grants to help enable participation in any of our workshops for mothers of young children. Recipients of these funds (available to women researchers with children 14 years old or under) can decide the best arrangement for themselves (e.g. support for companion caregivers or hired nannies here at Berkeley or to cover the costs of such help back at home) to ensure that their families are well cared for while they are able to focus on the Workshop activities.
Please note that because these funds are taxable, they are available only to U.S. Citizens and Permanent Residents. All recipients will be required to submit a completed W9 upon their arrival at MSRI.
MSRI is unable to offer any on-site childcare services in Berkeley, nor are we able to make recommendations for child care providers. For convenience, participants looking for childcare resources may find the following links useful:
- Bananas offers free referrals to licensed childcare providers and provides information and resources to families with young children.
- Berkeley Parents Network is an iconic website where parents can look for and recommend childcare.
MSRI Policies for Program and Workshop Participants
MSRI Collegiality Statement: MSRI is committed to fostering an atmosphere of respect, collegiality, and sensitivity. Please view the complete statement here.
MSRI Anti Discrimination and Harassment Policy: MSRI is committed to providing a welcoming environment free from discrimination on the basis of race, color, creed, religion, sex, national origin, age, physical or mental disability, family care status, veteran status, marital status, sexual orientation, identification or expression. Likewise, the Institute will not tolerate harassment based on these characteristics, or any form of sexual harassment. Please view the complete statement here.
This workshop will consist of introductory minicourses on key topics in Quantum Symmetry: fusion categories, modular tensor categories, Hopf algebras, subfactors and planar algebras, topological field theories, conformal nets, and topological phases of matter. These minicourses will be introductory and are aimed at giving semester participants exposure to the main ideas of subfields other than their own.Updated on Apr 09, 2018 02:20 PM PDT
This two-day workshop will survey notable developments in the foundations and applications of higher category theory. It will consist of two mini-courses given by emerging female leaders in the subject: Claudia Scheimbauer and Nathalie Wahl. This will be paired with a problem sessions lead by selected "TA's", themselves experts in higher structures. Each lecture series will be tailored to a diverse audience, accessible to graduate students and non-expert researchers with some background in homological algebra.
The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.Updated on Aug 01, 2019 04:20 PM PDT
This workshop will survey notable developments and applications of higher category theory; it will be a venue for end-users to share their vision of how to apply the theory, as well as developers to share technical advancements. It will consist of 6 series of 3 lectures, each given by instrumental end-users & developers of higher category theory, together with a few question-answer sessions. Each lecture series will be tailored to a diverse audience, accessible to graduate students and non-expert researchers with some background in homological also algebra. The content of these lecture series will concern the following topics.
Updated on Sep 14, 2018 02:08 PM PDT
- K-theory: categorification, non-commutative motives, trace methods;
- TQFT: functorial field theories, factorization homology.
- Parametrized higher category theory: stratifications, equivariant homotopy theory, operads, deformation theory and Koszul duality.
- Synthetic higher category theory: model-independent characterizations, cosmoi.
Sophisticated computational and quantitative techniques drive important decision-making in modern society. Such methods and algorithms are meant to improve the efficiency with which we work and the ways in which we live. An understanding of the mathematical underpinnings of these techniques can be used either to disrupt or to perpetuate inequities, and thus such knowledge constitutes power in the modern world. How does this powerful knowledge get used for the common good and get passed on to our children equitably? What does it imply about the kinds of mathematical skills, practices, and dispositions students should learn in schools, colleges, and universities?Updated on Dec 18, 2019 02:54 PM PST
The workshop will concern the latest developments in the mathematical study of quantum field theories. The focus will be on the interplay among topics such as higher category theory, as illustrated by the cobordism hypothesis, conformal field theory, tensor categories describing the quantum symmetries, and the relation to topological phases of matter.Updated on Dec 13, 2019 03:28 PM PST
This workshop will focus on recent developments in factorization homology, parametrized homotopy theory, and algebraic K-theory. These seemingly disparate topics are unified by a common methodology, which leverages universal properties and unforeseen descent by way of higher category theory. Furthermore, they enjoy powerful and complementary roles in application to the cyclotomic trace. This workshop will be a venue for experts in these areas to present new results, make substantive connections across fields, and suggest and contextualize outstanding questions and problems. It will consist of 9 speakers, each delivering a 1-hour morning talk and a 1-hour afternoon talk, in addition to a session reserved for drawing attention to an assortment of outstanding problems.Updated on Dec 13, 2019 03:28 PM PST
The goal of the workshop is to explore the many emerging connections between the theory of Optimal Transport and models and algorithms currently used in the Machine Learning community. In particular, the use of Wasserstein metrics and the relation between discrete models and their continuous counterparts will be presented and discussed.Updated on Jan 07, 2020 08:47 AM PST
The two topics, combinatorial theory of free resolutions and differential graded algebra techniques in homological algebra, each have a long and rich history in commutative algebra and its applications to algebraic geometry. Free resolutions are at the center of much of the study in the field and these two approaches give powerful tools for their study and their application to other problems. Neither of these topics is generally covered in graduate courses. Furthermore, recent developments have exhibited exciting interplay between the two subjects. The purpose of the school is to introduce the graduate students to these subjects and these new developments. The school will consist of two lectures each day and carefully planned problem sessions designed to reinforce the foundational material and to give them a chance to experiment with problems involving the interplay between the two subjects.Updated on Jul 26, 2019 03:43 PM PDT
The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.
In 2020, MSRI-Up will focus on Branched Covers of Curves. The research program will be led by Dr. Edray Goins, Professor of Mathematics at Pomona College.Updated on Dec 10, 2019 09:18 AM PST
[The image on this vase from Minoan Crete, dated on 1500-2000 BC, resembles an ancient solution to the Curve shortening flow - one of the most basic geometric flows. The vase is at Heraklion Archaeological Museum]
This summer graduate school is a collabroation between MSRI and the FORTH-IACM Institute in Crete. The purpose of the school is to introduce graduate students to some of the most important geometric evolution equations.
This is an area of geometric analysis that lies at the interface of differential geometry and partial differential equations. The lectures will begin with an introduction to nonlinear diffusion equations and continue with classical results on the Ricci Flow, the Mean curvature flow and other fully non-linear extrinsic flows such as the Gauss curvature flow. The lectures will also include geometric applications such as isoperimetric inequalities, topological applications such as the Poincaré onjecture, as well as recent important developments related to the study of singularities and ancient solutions.Updated on Jan 23, 2020 12:15 PM PST
The purpose of the summer school will be to introduce graduate students to effective methods in algebraic theories of differential and difference equations with emphasis on their model-theoretic foundations and to demonstrate recent applications of these techniques to studying dynamic models arising in sciences. While these topics comprise a coherent and rich subject, they appear in graduate coursework in at best a piecemeal way, and then only as components of classes for other aims. With this Summer Graduate School, students will learn both the theoretical basis of differential and difference algebra and how to use these methods to solve practical problems. Beyond the lectures, the graduate students will meet daily in problem sessions and will participate in one-on-one mentoring sessions with the lecturers and organizers.Updated on Jan 16, 2020 11:37 AM PST
Representation Theory has undergone a revolution in recent years, with the development of what is now known as higher representation theory. In particular, the notion of categorification has led to the resolution of many problems previously considered to be intractable.
The school will begin by providing students with a brief but thorough introduction to what could be termed the “bread and butter of modern representation theory”, i.e., compact Lie groups and their representation theory; character theory; structure theory of algebraic groups.
We will then continue on to a number of more specialized topics. The final mix will depend on discussions with the prospective lecturers, but we envisage such topics as:
• modular representation theory of finite groups (blocks, defect groups, Broué’s conjecture);
• perverse sheaves and the geometric Satake correspondence;
• the representation theory of real Lie groups.Updated on Aug 08, 2019 09:36 AM PDT
The topic of random graphs is at the forefront of applied probability, and it is one of the central topics in multidisciplinary science where mathematical ideas are used to model and understand the real world. At the same time, random graphs pose challenging mathematical problems that have attracted the attention from probabilists and combinatorialists since the 1960, with the pioneering work of Erdös and Rényi. Around the turn of the millennium, very large data sets started to become available, and several applied disciplines started to realize that many real-world networks, even though they are from various different origins, share many fascinating features. In particular, many of such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scalefree, in the sense that there are enormous differences in the number of connections that their elements make. In particular, such networks are quite different from the classical random graph models, such as proposed by Erdös and Rényi.Updated on Jul 26, 2019 03:40 PM PDT
Probability theory, statistics as well as mathematical physics have increasingly been used in computer science. The goal of this school is to provide a unique opportunity for graduate students and young researchers to developed multi-disciplinary skills in a rapidly evolving area of mathematics.
The topics would include spin glasses, constraint satisfiability, randomized algorithms, Monte-Carlo Markov chains and high-dimensional statistics, sparse and random graphs, computational complexity, estimation and approximation algorithms. Those topics will fall into two main categories, on the one hand problems related to spin glasses and on the other hand random algorithms.
The part of the summer school dedicated to spin glasses will be split into three parts: an introductory course about traditional spin glasses followed by two more advanced courses where spin glasses meet computer science in addition to a talk on dynamics of spin glasses. The part of the summer school on random algorithms will consist of an introductory course on phase transitions in large random structures, followed by advanced courses on theoretical bounds for computational complexity in reconstruction and inference, and on understanding rare events in random graphs and models of statistical mechanics.
The two introductory courses on spin glasses and on random algorithms will be accompanied by three exercises sessions of one hour. A one hour exercises session will follow each of the three sessions of a course for both the introductory course on spin glasses and the introductory course on random algorithms. Exercises sessions will be led by an assistant, but will primarily focus on participation of the students.Updated on Jan 16, 2020 02:57 PM PST
[Image: The simplest interesting case of linkage (liaison) of curves in projective 3-space. We see two quadric surfaces, one of which is a cone, meeting in the union of a line (vertical in the illustration) and a twisted cubic (snaking up from the bottom left to the upper right, tangent to the line at the origin.]
The theory of algebraic curves, arguably the oldest branch of algebraic geometry, has seen major developments in recent years, for example in the study of syzygies, and around questions about moduli spaces and Hilbert schemes of curves. The theory is rich in research activity and unsolved problems. There is an encyclopedic work by Arbarello, Cornalba, Griffiths and Harris, but there is no modern text that could be used as a textbook and that goes beyond the basics of the theory. We have embarked on a project to write a book at roughly the level of the wonderful book on complex algebraic surfaces by Arnaud Beauville. The intent can be seen from a list of some major topics it will treat:
- Linear series and Brill-Noether theory
- Personalities: curves in projective space with low genus and degree
- Overview of moduli and Jacobians
- Hilbert schemes
- Syzygies and linkage
The school will have two series of lectures, one by Harris and one by Eisenbud. Harris’ lectures will focus on the more geometric side of the theory, including Brill-Noether theory, families of curves and Jacobians; while Eisenbud’s lectures will focus on the more algebraic side of the theory, including properties of the homogeneous coordinate rings of curves (Cohen-Macaulay, Gorenstein, free resolutions, scrolls, ...) Both lecturers will rely on chapters from the forthcoming book, which should be finished in large part by the time of the school. In addition, some of Eisenbud’s lectures will treat the use of Macaulay2 to investigate the projective embeddings of curves.Updated on Aug 14, 2019 03:45 PM PDT
Proofs are at the foundations of mathematics. Viewed through the lens of theoretical computer science, verifying the correctness of a mathematical proof is a fundamental computational task. Indeed, the P versus NP problem, which deals precisely with the complexity of proof verification, is one of the most important open problems in all of mathematics.
The complexity-theoretic study of proof verification has led to exciting reenvisionings of mathematical proofs. For example, probabilistically checkable proofs (PCPs) admit local-to-global structure that allows verifying a proof by reading only a minuscule portion of it. As another example, interactive proofs allow for verification via a conversation between a prover and a verifier, instead of the traditional static sequence of logical statements. The study of such proof systems has drawn upon deep mathematical tools to derive numerous applications to the theory of computation and beyond.
In recent years, such probabilistic proofs received much attention due to a new motivation, delegation of computation, which is the emphasis of this summer school. This paradigm admits ultra-fast protocols that allow one party to check the correctness of the computation performed by another, untrusted, party. These protocols have even been realized within recently-deployed technology, for example, as part of cryptographic constructions known as succinct non-interactive arguments of knowledge (SNARKs).
This summer school will provide an introduction to the field of probabilistic proofs and the beautiful mathematics behind it, as well as prepare students for conducting cutting-edge research in this area.Updated on Nov 21, 2019 11:41 AM PST
The purpose of the summer school is to introduce graduate students to key mainstream directions in the recent development of geometry, which sprang from Riemannian Geometry in an attempt to use its methods in various contexts of non-smooth geometry. This concerns recent developments in metric generalizations of the theory of nonpositively curved spaces and discretizations of methods in geometry, geometric measure theory and global analysis. The metric geometry perspective gave rise to new results and problems in Riemannian Geometry as well.
All these themes are intertwined and have developed either together or greatly influencing one another. The summer school will introduce some of the latest developments and the remaining open problems in these very modern areas, and will emphasize their synergy.Updated on Jul 31, 2019 11:07 AM PDT
The study of nonnegative polynomials and sums of squares is a classical area of real algebraic geometry dating back to Hilbert’s 17th problem. It also has rich connections to real analysis via duality and moment problems. In the last 15 years, sums of squares relaxations have found a wide array of applications from very applied areas (e.g., robotics, computer vision, and machine learning) to theoretical applications (e.g., extremal combinatorics, theoretical computer science). Also, an intimate connection between sums of squares and classical algebraic geometry has been found. Work in this area requires a blend of ideas and techniques from algebraic geometry, convex geometry and representation theory. After an introduction to nonnegative polynomials, sums of squares and semidefinite optimization, we will focus on the following three topics:
- Sums of squares on real varieties (sets defined by real polynomial equations) and connections with classical algebraic geometry.
- Sums of squares method for proving graph density inequalities in extremal combinatorics. Here addition and multiplication take place in the gluing algebra of partially labelled graphs.
- Sums of squares relaxations for convex hulls of real varieties and theta-bodies with applications in optimization.
The summer school will give a self-contained introduction aimed at beginning graduate students, and introduce participants to the latest developments. In addition to attending the lectures, students will meet in intensive problem and discussion sessions that will explore and extend the topics developed in the lectures.Updated on Jul 26, 2019 03:40 PM PDT
The purpose of this two weeks school is to introduce graduate students to the state of the art methods and results in the study of incompressible Euler’s equations in general, and water waves in particular. This is a research area which is highly relevant to many real life problems, and in which substantial progress has been made in the last decade.
The goal is to present the main current research directions in water waves. We will begin with the physical derivation of the equations, and present some of the analytic tools needed in study. The final goal will be two-fold, namely (i) to understand the local solvability of the Cauchy problem for water waves, as well as (ii) to describe the long time behavior of solutions.
Through the lectures and associated problem sessions, students will learn about a number of new analysis tools which are not routinely taught in a graduate school curriculum. The goal is to help students acquire the knowledge needed in order to start research in water waves and Euler equations.Updated on Jul 26, 2019 03:40 PM PDT
The aim of the workshop is to discover how the problems in number theory and algebraic geometry arising from the Hilbert’s tenth problem for rationals interact with the ideas and techniques in mathematical logic, such as definability from model theory and decidability and degree-theoretic complexity from computability theory. This interaction includes various analogues of Hilbert’s tenth problem and related questions, focusing on the connections of algebraic, number-theoretic, model-theoretic, and computability-theoretic properties of structures and objects in algebraic number theory, anabelian geometry, field arithmetic, and differential algebra.Updated on Apr 11, 2019 01:47 PM PDT
Our workshop will focus research efforts on the interaction of number-theoretic questions with questions of decidability, definability, and computability, bringing together researchers approaching these questions from various sides to work on the core issues. This Introductory Workshop will serve as the introductory event of the MSRI semester program and is designed to introduce the basic structures and ideas of the different communities, and to highlight problems of active current interest.Updated on Apr 23, 2019 01:30 PM PDT
This two-day workshop will consist of various talks given by prominent female mathematicians in the field. These will be appropriate for graduate students, post-docs, and researchers in areas related to the program. The workshop will also include a professional development session.
This workshop is open to all mathematicians.Updated on Jun 12, 2018 09:17 AM PDT
The use of dynamical invariants has long been a staple of geometry and topology, from rigidity theorems, to classification theorems, to the general study of lattices and of the mapping class group. More recently, random structures in topology and notions of probabilistic geometric convergence have played a critical role in
testing the robustness of conjectures in the arithmetic setting.
In this introductory workshop, we will bring together junior and senior researchers in order to provide a mix of introductory lectures as well as reporting on more recent progress in topics from this diverse range of subjects.Updated on Jun 17, 2019 08:13 AM PDT
The study of discrete subgroups of Lie groups and the associated locally symmetric manifolds has a long and rich history, with powerful interconnections between the geometry of the locally symmetric space, topology of towers of its finite covers, and number-theoretic aspects. More recently dynamical and probabilistic techniques have been fruitfully employed to study these groups and spaces. The workshop will take stock of recent developments in these highly active fields from a variety of backgrounds.Updated on Jun 06, 2019 09:08 AM PDT
The workshop will address topics in the PDE analysis of the basic equations of the incompressible fluid dynamics (the Euler equations for inviscid flows, the Navier Stokes equations for viscous flows), interface problems (water waves), and other related equations. Open problems and connections to related branches of mathematics will be discussed, including the phenomena of turbulence and the zero viscosity limit. Both theoretical and numerical aspects of these topics will be considered. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.Updated on Nov 25, 2019 01:09 PM PST
The aim of the workshop is to bring together a broad array of researchers working on incompressible fluid dynamics. Some of the key topics to be covered are Euler flows, Navier Stokes equations as well as water wave flows and associated model equations. Some emphasis will also be placed on numerical analysis of the above evolutions.Updated on Jun 18, 2019 09:54 AM PDT
The talks in this workshop will present a wide array of current applications of topology in neuroscience, including classification and synthesis of neuron morphologies, analysis of synaptic plasticity, algebraic analysis of the neural code, topological analysis of neural networks and their dynamics, topological decoding of neural activity, diagnosis of traumatic brain injuries, and topological biomarkers for psychiatric disease. Some of the talks will be devoted to promising new directions in algebraic topology that have been inspired by neuroscience.Updated on Nov 27, 2019 01:57 PM PST
This workshop will focus on the integrable aspect of random matrix theory and other related probability models such as random tilings, directed polymers, and interacting particle systems. The emphasis is on communicating diverse algebraic structures in these areas which allow the asymptotic analysis possible. Some of such structures are determinantal point processes, Toeplitz and Hankel determinants, Bethe ansatz, Yang-Baxter equation, Karlin-McGregor formula, Macdonald process, and stochastic six vertex model.Updated on Jul 31, 2019 03:22 PM PDT
This workshop will feature several talks by experts, along with numerous 5-minute presentations by junior mathematicians, on topics related to Quantum Symmetry. Such topics will include tensor categories, subfactors, Hopf algebras, topological quantum field theory and more. There will also be a panel discussion on professional development. The majority of the speakers and panelists for this event will be women and gender minorities, and members of these groups and of other underrepresented groups are especially encouraged to attend. This workshop is open to all mathematicians.Updated on Jan 24, 2020 10:25 AM PST
MSRI will host a Symposium on the occasion of Julia Robinson’s 100th birthday on Monday, December 9, 2019 at MSRI. Julia Robinson (1919-1985) was an internationally renowned logician of the twentieth century. She was a trailblazer in mathematics as well as in many other ways: she was the first woman president of the American Mathematical Society, and the first woman mathematician elected to membership in the National Academy of Sciences.
Participating speakers in this day-long celebration of her work and of current mathematics insprired by her research include: Martin Davis, Kirsten Eisentrager, Yuri Matiyasevich, and Lou van den Dries. Following the symposium, Lenore Blum will give a public lecture at UC Berkeley.Updated on Nov 22, 2019 03:54 PM PST
Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In some cases the areas themselves (such as stability conditions on Fukaya-type categories, links to quantum integrable systems, or the physically derived construction of so-called spectral networks) are new, while in others the novelty lies more in the role of the holomorphic differentials (for example in the study of billiards in polygons, special - Hitchin or higher Teichmuller - components of representation varieties, asymptotic properties of Higgs bundle moduli spaces, or in new interactions with algebraic geometry).
It is remarkable how widely scattered are the motivating questions in these areas, and how diverse are the backgrounds of the researchers pursuing them. Bringing together experts in this wide variety of fields to explore common interests and discover unexpected connections is the main goal of our program. Our workshop will be of interest to those working in many different fields, including low-dimensional dynamical systems (via the connection to billiards); differential geometry (Higgs bundles and related moduli spaces); and different types of theoretical physics (electron transport and supersymmetric quantum field theory).Updated on Nov 21, 2019 10:44 AM PST
As part of the Mathematical Sciences Collaborative Diversity Initiatives, six mathematics institutes are pleased to host their annual SACNAS pre-conference event, the 2019 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 PhDs in building their research networks.Updated on Dec 18, 2019 02:42 PM PST
Elwyn Berlekamp (1937-2019) was a pioneering contributor to combinatorial game theory, greatly advancing the subject over the course of a more than five-decade career. Along with his coauthors, John Conway and Richard Guy, Berlekamp invented the modern form of the theory, with the publication of Winning Ways for Your Mathematical Plays in 1982. His later work substantially advanced our understanding of the mathematical structure of well-known games such as Go, Amazons, and Dots-and-Boxes. More information about his life can be found at www.msri.org/elwyn.
This workshop will be an informal two-day mini-conference honoring Berlekamp's work and the subject he helped create. The event will consist of talks, afternoon workshops, and a combinatorial games tournament.Updated on Aug 28, 2019 06:09 PM PDT
Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory, hyperbolic dynamical systems, probability… As this description shows microlocal analysis has become a very broad area. Due to its breadth, it is a challenge for researchers to be aware of what is happening in other parts of the field, and the impact this may have in their own research area. The purpose of this workshop is thus to bring together researchers from different parts of microlocal analysis and its applications to facilitate the transfer of new ideas.Updated on Dec 05, 2019 10:59 AM PST
The objective of the meeting is to bring theorists and theoretically-motivated experimentalists together to discuss promising theoretical frameworks for understanding cognitive processes and how these may be brought to bear on interpreting neural data or formulating new experiments. We hope that this meeting will be a chance to discuss future goals for theory in neuroscience: what are missing areas and emerging approaches that might help the field to make real progress in developing theories of brain function.Updated on Jul 26, 2019 01:00 PM PDT
Microlocal analysis provides tools for the precise analysis of problems arising in areas such as partial differential equations or integral geometry by working in the phase space, i.e. the cotangent bundle, of the underlying manifold. It has origins in areas such as quantum mechanics and hyperbolic equations, in addition to the development of a general PDE theory, and has expanded tremendously over the last 40 years to the analysis of singular spaces, integral geometry, nonlinear equations, scattering theory… This workshop will provide a comprehensive introduction to the field for postdocs and graduate students as well as specialists outside the field, building up from standard facts about the Fourier transform, distributions and basic functional analysis.Updated on Sep 05, 2019 01:10 PM PDT
This workshop will provide a gentle introduction to a selection of applications of microlocal analysis. These may be drawn from among geometric microlocal analysis, inverse problems, scattering theory, hyperbolic dynamical systems, quantum chaos and relativity. The workshop will also provide a panel discussion, a poster session and an introduction/research session.
This workshop is open to all mathematicians.Updated on Sep 24, 2019 09:45 AM PDT
Holomorphic differentials on Riemann surfaces have long held a distinguished place in low dimensional geometry, dynamics and representation theory. Recently it has become apparent that they constitute a common feature of several other highly active areas of current research in mathematics and also at the interface with physics. In this introductory workshop, we will bring junior and senior researchers from this diverse range of subjects together in order to explore common themes and unexpected connections.Updated on Aug 22, 2019 10:50 AM PDT
This two-day workshop will consist of various talks given by prominent female mathematicians on topics of new developments in the role of holomorphic differentials on Riemann surfaces. These will be appropriate for graduate students, post-docs, and researchers in areas related to the program.
This workshop is open to all mathematicians.Updated on Sep 24, 2019 09:48 AM PDT
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
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
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
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
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
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
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
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
The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.
In 2019, MSRI-Up will focus on the application of combinatorial arguments and techniques to enumerate, examine, and investigate the existence of discrete mathematical structures with certain properties. The areas of interest for these applications encompass a wide range of mathematical fields and will include algebra, number theory, and graph theory, through weight multiplicity computations, the study of vector partition functions, and graph domination problems, respectively. The research program will be led by Dr. Pamela E. Harris, Assistant Professor of Mathematics at Williams College.Updated on Sep 25, 2019 03:58 PM PDT
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
Is your department interested in helping graduate students learn to teach? Perhaps your department is considering starting a teaching-focused professional development program. Or maybe your department has a program but is interested in updating and enhancing it.
Many departments now offer pre-semester orientations, semester-long seminars, and other opportunities for graduate students who are new to teaching so they will be well-equipped to provide high-quality instruction to undergraduates. The purpose of this workshop is to support faculty from departments that are considering starting a teaching-focused professional development program or, for departments that have a program, to learn ways to improve it.Updated on Mar 04, 2019 04:57 PM PST
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 field. 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
Updated on May 29, 2019 09:11 AM PDT
- Linkage and residual intersections
- Characteristic p methods and applications
- Blowup algebras
- Multiplicity theory
This workshop will be focused on presenting the latest developments in moduli theory, including (but not restricted to) recent advances in compactifications of moduli spaces of higher dimensional varieties, the birational geometry of moduli spaces, abstract methods including stacks, stability criteria, and applications in other disciplines.Updated on Sep 24, 2019 09:45 AM PDT
GOAL: To highlight careers and opportunities in the mathematical sciences, and to prepare women
and underrepresented minorities for work in academia, industry, and government laboratories.Updated on Mar 08, 2019 11:08 AM PST
The purpose of the workshop is to explain Vincent Lafforgue's ground breaking work, constructing the automorphic to Galois direction of the Langlands correspondence for function fields. There will also be a number of talks on more recent developments and related results.Updated on Sep 24, 2019 09:46 AM PDT
This workshop will bring together researchers at various frontiers, including arithmetic geometry, representation theory, mathematical physics, and homotopy theory, where derived algebraic geometry has had recent impact. The aim will be to explain the ideas and tools behind recent progress and to advertise appealing questions. A focus will be on moduli spaces, for example of principal bundles with decorations as arise in many settings, and their natural structures.Updated on Sep 24, 2019 09:46 AM PDT
Mathematical Modeling (MM) now has increased visibility in the education system and in the public domain. It appears as a content standard for high school mathematics and a mathematical practice standard across the K-12 curriculum (Common Core Standards; and other states’ standards in mathematics education). Job opportunities are increasing in business, industry and government for those trained in the mathematical sciences. Quantitative reasoning is foundational for civic engagement and decision-making for addressing complex social, economic, and technological issues. Therefore, we must take action to support and sustain a significant increase in the teaching and learning of mathematical modeling from Kindergarten through Graduate School.
Mathematical modeling is an iterative process by which mathematical concepts and structures are used to analyze or gain qualitative and quantitative understanding of real world situations. Through modeling students can make genuine mathematical choices and decisions that take into consideration relevant contexts and experiences.
Mathematical modeling can be a vehicle to accomplish multiple pedagogical and mathematical goals. Modeling can be used to introduce new material, solidify student understanding of previously learned concepts, connect the world to the classroom, make concrete the usefulness (maybe even the advantages) of being mathematically proficient, and provide a rich context to promote awareness of issues of equity, socio-political injustices, and cultural relevance in mathematics.
A critical issue in math education is that although mathematical modeling is part of the K-12 curriculum, the great majority of teachers have little experience with mathematical modeling as learners of mathematics or in their teacher preparation. In some cases, mathematics teacher educators have limited experience with mathematical modeling while being largely responsible for preparing future teachers.
Currently, the knowledge in teaching and learning MM is underdeveloped and underexplored. Very few MM resources seem to reach the K-16 classrooms. Collective efforts to build a cohesive curriculum in MM and exploration of effective teaching practices based on research are necessary to make mathematical modeling accessible to teacher educators, teachers and students.
At the undergraduate level, mathematical modeling has traditionally been reserved for university courses for students in STEM majors beyond their sophomore year. Many of these courses introduce models but limit the students’ experience to using models that were developed by others rather than giving students the opportunity to generate their own models as is common in everyday life, in modeling competitions and in industry.
The CIME workshop on MM will bring together mathematicians, teacher educators, K-12 teachers, faculty and people in STEM disciplines. As partners we can address ways to realize mathematical modeling in the K-12 classrooms, teacher preparation, and lower and upper division coursework at universities. The content and pedagogy associated with teaching mathematical modeling needs special attention due to the nature of modeling as a process and as a body of content knowledge.Updated on Sep 24, 2019 09:46 AM PDT
The workshop will survey several areas of algebraic geometry, providing an introduction to the two main programs hosted by MSRI in Spring 2019. It will consist of 7 expository mini-courses and 7 separate lectures, each given by top experts in the field.The focus of the workshop will be the recent progress in derived algebraic geometry, birational geometry and moduli spaces. The lectures will be aimed at a wide audience including advanced graduate students and postdocs with a background in algebraic geometry.Updated on Sep 24, 2019 09:47 AM PDT
This workshop will be on different aspects of Algebraic Geometry relating Derived Algebraic Geometry and Birational Geometry. In particular the workshop will focus on connections to other branches of mathematics and open problems. There will be some colloquium style lectures as well as shorter research talks. The workshop is open to all.Updated on Sep 24, 2019 09:47 AM PDT