
Workshop Critical Issues in Mathematics Education 2020: Today’s Mathematics, Social Justice, and Implications for Schools
Organizers: Meredith Broussard (New York Unviersity), Victor Donnay (Bryn Mawr College), Courtney Ginsberg (Math for America), Luis Leyva (Vanderbilt University), Chris Rasmussen (San Diego State University), LEAD Katherine Stevenson (California State University, Northridge), William Tate (Washington University in St. Louis)Sophisticated computational and quantitative techniques drive important decisionmaking 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 Oct 22, 2019 09:10 AM PDT 
Summer Graduate School Combinatorial and DGAlgebra Techniques for Free Resolutions (Tianjin, China)
Organizers: Chengming Bai (Chern Institute of Mathematics), LEAD Dave Bayer (Columbia University), Claudia Miller (Syracuse University)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 
MSRIUP MSRIUP 2020: Branched Covers of Curves
Organizers: Federico Ardila (San Francisco State University), LEAD Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI  Mathematical Sciences Research Institute), Rebecca Garcia (Sam Houston State University), Edray Goins (Pomona College), Suzanne Weekes (Worcester Polytechnic Institute)The MSRIUP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.
In 2020, MSRIUp 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 Nov 25, 2019 12:23 PM PST 
Summer Graduate School Algebraic Theory of Differential and Difference Equations, Model Theory and their Applications
Organizers: LEAD Alexey Ovchinnikov (City University of New York (CUNY)), Anand Pillay (University of Notre Dame), Gleb Pogudin (New York University, Courant Institute), Thomas Scanlon (University of California, Berkeley), Michael Wibmer (University of Notre Dame)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 modeltheoretic 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 oneonone mentoring sessions with the lecturers and organizers.
Updated on Jul 26, 2019 03:42 PM PDT 
Summer Graduate School Geometric Flows (Athens, Greece)
Organizers: Nicholas Alikakos (National and Kapodistrian University of Athens (University of Athens)), Panagiota Daskalopoulos (Columbia University)[The image on this vase from Minoan Crete, dated on 15002000 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 FORTHIACM 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 nonlinear 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 Dec 06, 2019 02:28 PM PST 
Summer Graduate School Séminaire de Mathématiques Supérieures 2020: Discrete Probability, Physics and Algorithms (Montréal, Canada)
Organizers: Gerard Ben Arous (New York University, Courant Institute), LEAD Alexander Fribergh (University of Montreal), Lea Popovic (Concordia University)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 multidisciplinary skills in a rapidly evolving area of mathematics.
The topics would include spin glasses, constraint satisfiability, randomized algorithms, MonteCarlo Markov chains and highdimensional 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 Sep 18, 2019 03:30 PM PDT 
Summer Graduate School Random Graphs
Organizers: Louigi AddarioBerry (McGill University), Remco van der Hofstad (Technische Universiteit Eindhoven)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 realworld 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 
Summer Graduate School Algebraic Curves (Hainan, China)
Organizers: David Eisenbud (MSRI  Mathematical Sciences Research Institute), Joseph Harris (Harvard University)[Image: The simplest interesting case of linkage (liaison) of curves in projective 3space. 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 BrillNoether 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 BrillNoether 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 (CohenMacaulay, 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 
Summer Graduate School Foundations and Frontiers of Probabilistic Proofs (Zurich, Switzerland)
Organizers: Alessandro Chiesa (University of California, Berkeley), Tom Gur (University of Warwick)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 complexitytheoretic study of proof verification has led to exciting reenvisionings of mathematical proofs. For example, probabilistically checkable proofs (PCPs) admit localtoglobal 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 ultrafast protocols that allow one party to check the correctness of the computation performed by another, untrusted, party. These protocols have even been realized within recentlydeployed technology, for example, as part of cryptographic constructions known as succinct noninteractive 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 cuttingedge research in this area.
Updated on Nov 21, 2019 11:41 AM PST 
Summer Graduate School New Directions in Representation Theory (AMSI, Brisbane, Australia)
Organizers: Tim Brown (Australian Mathematical Sciences Institute), Joseph Grotowski (University of Queensland), Chloe Pearse (Australian Mathematical Sciences Institute), Jacqui Ramagge (University of Sydney), Ole Warnaar (University of Queensland), Geordie Williamson (University of Sydney)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 
Summer Graduate School Metric Geometry and Geometric Analysis (Oxford, United Kingdom)
Organizers: LEAD Cornelia Drutu (University of Oxford), Panos Papazoglou (University of Oxford)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 nonsmooth 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 
Summer Graduate School Sums of Squares Method in Geometry, Combinatorics and Optimization
Organizers: LEAD Grigoriy Blekherman (Georgia Institute of Technology), Annie Raymond (University of Massachusetts Amherst), Rekha Thomas (University of Washington)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 thetabodies with applications in optimization.
The summer school will give a selfcontained 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 
Summer Graduate School Introduction to water waves
Organizers: Mihaela Ifrim (University of WisconsinMadison), Daniel Tataru (University of California, Berkeley)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 twofold, 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
Past Educational Events

Workshop Symposium in Honor of Julia Robinson’s 100th Birthday
Organizers: Hélène Barcelo (MSRI  Mathematical Sciences Research Institute), Thomas Scanlon (University of California, Berkeley), Carol Wood (Wesleyan University)MSRI will host a Symposium on the occasion of Julia Robinson’s 100th birthday on Monday, December 9, 2019 at MSRI. Julia Robinson (19191985) 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 daylong 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 
Workshop Modern Math Workshop 2019
Organizers: Sudipta Dasmohapatra (Duke University ), Christian Ratsch (University of California, Los Angeles; Institute of Pure and Applied Mathematics (IPAM)), Michael Singer (MSRI  Mathematical Sciences Research Institute), Ulrica Wilson (Morehouse College; Institute for Computational and Experimental Research in Mathematics (ICERM))As part of the Mathematical Sciences Collaborative Diversity Initiatives, six mathematics institutes are pleased to host their annual SACNAS preconference 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 Nov 25, 2019 11:56 AM PST 
Summer Graduate School Toric Varieties (National Center for Theoretical Sciences, Taipei)
Organizers: David Cox (Amherst College), Henry Schenck (Auburn University)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 
Summer Graduate School HPrinciple (INdAM, Cortona, Italy)
Organizers: LEAD Emmy Murphy (Northwestern University), Takashi Tsuboi (University of Tokyo)This two week summer school will introduce graduate students to the theory of hprinciples. 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 
Summer Graduate School Mathematics of Machine Learning
Organizers: Sebastien Bubeck (Microsoft Research), Anna Karlin (University of Washington), Adith Swaminathan (Microsoft Research)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 
Summer Graduate School Recent topics on wellposedness 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)The purpose of the workshop is to introduce graduate students to fundamental results on the NavierStokes 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 
Summer Graduate School Polynomial Method
Organizers: Adam Sheffer (Bernard M. Baruch College, CUNY), LEAD Joshua Zahl (University of British Columbia)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 
Summer Graduate School 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)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 fourdimensional 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 
Summer Graduate School Geometric Group Theory
Organizers: LEAD Rita Jiménez Rolland (Instituto de Matematicás, UNAMOaxaca), LEAD Pierre Py (Instituto de Matematicás, UNAMCiudad Universitaria)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 
Summer Graduate School Representation stability
Organizers: Thomas Church (Stanford University), LEAD Andrew Snowden (University of Michigan), Jenny Wilson (University of Michigan)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 
MSRIUP MSRIUP 2019: Combinatorics and Discrete Mathematics
Organizers: Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI  Mathematical Sciences Research Institute), LEAD Rebecca Garcia (Sam Houston State University), Pamela Harris (Williams College), Suzanne Weekes (Worcester Polytechnic Institute)The MSRIUP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.
In 2019, MSRIUp 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 
Summer Graduate School 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 numbertheoretic 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 
Workshop Improving the Preparation of Graduate Students to Teach Undergraduate Mathematics
Organizers: Jack Bookman (Duke University), Shandy Hauk (WestEd), LEAD Dave Kung (St. Mary's College of Maryland), LEAD Natasha Speer (University of Maine)Is your department interested in helping graduate students learn to teach? Perhaps your department is considering starting a teachingfocused professional development program. Or maybe your department has a program but is interested in updating and enhancing it.
Many departments now offer presemester orientations, semesterlong seminars, and other opportunities for graduate students who are new to teaching so they will be wellequipped to provide highquality instruction to undergraduates. The purpose of this workshop is to support faculty from departments that are considering starting a teachingfocused 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 
Summer Graduate School 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)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 pth 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 BrianconSkoda type theorems for equicharacteristic 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 HilbertSamuel and the BuchsbaumRim 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
 Linkage and residual intersections
 Characteristic p methods and applications
 Blowup algebras
 Multiplicity theory
Updated on May 29, 2019 09:11 AM PDT 
Workshop Critical Issues in Mathematics Education 2019: Mathematical Modeling in K16: Community and Cultural Contexts
Organizers: Julia Aguirre (University of Washington  Tacoma), LEAD Cynthia Anhalt (University of Arizona), Staffas Broussard (The Algebra Project), Ricardo Cortez (Tulane University), Michael Driskill (Math for America ), Sol Garfunkel (Consortium for Mathematics and Its Applications (COMAP)), Genetha Gray (Salesforce), Maria Hernandez (North Carolina School of Science and Mathematics), LEAD Rachel Levy (MAA  Mathematical Association of America), Javier Rojo (Oregon State)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 K12 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 decisionmaking 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, sociopolitical injustices, and cultural relevance in mathematics.
A critical issue in math education is that although mathematical modeling is part of the K12 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 K16 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, K12 teachers, faculty and people in STEM disciplines. As partners we can address ways to realize mathematical modeling in the K12 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 
Workshop 2018 BlackwellTapia Conference and Award Banquet
The NSF Mathematical Sciences Institutes Diversity Committee hosts the 2018 BlackwellTapia Conference and Awards Ceremony. This is the ninth conference since 2000, held every other year, with the location rotating among NSF Mathematics Institutes. The conference and prize honors David Blackwell, the first AfricanAmerican member of the National Academy of Science, and Richard Tapia, winner of the National Medal of Science in 2010, two seminal figures who inspired a generation of AfricanAmerican, Native American and Latino/Latina students to pursue careers in mathematics. The BlackwellTapia Prize recognizes a mathematician who has contributed significantly to research in his or her area of expertise, and who has served as a role model for mathematical scientists and students from underrepresented minority groups, or has contributed in other significant ways to addressing the problem of underrepresentation of minorities in math.
The 2018 recipient of the BlackwellTapia Prize is Dr. Ronald E. Mickens, the Distinguished Fuller E. Callaway Professor in the Department of Physics at Clark Atlanta University.
The conference will include scientific talks, poster presentations, panel discussions, ample opportunities for networking, and the awarding of the BlackwellTapia Prize. Participants are invited from all career stages and will represent institutions of all sizes across the country, including Puerto Rico.
Updated on May 08, 2018 12:46 PM PDT 
Workshop 2018 Modern Math Workshop
Organizers: Hélène Barcelo (MSRI  Mathematical Sciences Research Institute), LEAD Elvan Ceyhan (SAMSI  Statistical and Applied Mathematical Sciences Institute), Leslie McClure (SAMSI  Statistical and Applied Mathematical Sciences Institute), Christian Ratsch (University of California, Los Angeles; Institute of Pure and Applied Mathematics (IPAM)), Ulrica Wilson (Morehouse College; Institute for Computational and Experimental Research in Mathematics (ICERM))The Mathematical Sciences Diversity Initiative holds a Modern Math Workshop (MMW) prior to the SACNAS National Conference each year. The 2018 MMW will be hosted by SAMSI at the Henry B. Gonzalez Convention Center, San Antonio, Texas on October 10th and 11th, 2018. This workshop is intended to encourage undergraduates, graduate students and recent PhDs from underrepresented minority groups to pursue careers in the mathematical sciences and build research and mentoring networks. The Modern Math Workshop is a preconference event at the SACNAS National Conference. The MMW includes a keynote lecture, minicourses, research talks, a question and answer session and a reception.
Updated on Mar 15, 2018 12:33 PM PDT 
Summer Graduate School 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 stateoftheart 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 
Summer Graduate School 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. Handson topics will include data mining, compression, classification, topic modeling, largescale stochastic optimization, and more.Updated on Jul 19, 2018 11:45 AM PDT 
Summer Graduate School 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 minicourses 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 
Summer Graduate School 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 
Summer Graduate School Hprinciple
Organizers: Emmy Murphy (Northwestern University), Takashi Tsuboi (University of Tokyo)This two week summer school will introduce graduate students to the theory of hprinciples. 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 
Summer Graduate School 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 1520 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 
MSRIUP MSRIUP 2018: The Mathematics of Data Science
Organizers: Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), LEAD Maria Franco (Queensborough Community College (CUNY); MSRI  Mathematical Sciences Research Institute), Rebecca Garcia (Sam Houston State University), David Uminsky (University of San Francisco), Suzanne Weekes (Worcester Polytechnic Institute)The MSRIUP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.
In 2018, MSRIUP will focus on the core role of (linear) algebra in current research and application areas of Data Science ranging from unsupervised learning, clustering and networks, to algebraic signal processing and feature extraction, to the central role linear algebra plays in deep machine learning. The research program will be led by Dr. David Uminsky, Associate Professor of Mathematics and Statistics at the University of San Francisco.
Updated on Aug 02, 2018 09:47 AM PDT 
Summer Graduate School The ∂Problem in the TwentyFirst 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 CauchyRiemann 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 selfcontained and the prerequisites will be kept at a minimum
Updated on Jun 21, 2018 01:13 PM PDT 
Summer Graduate School 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