
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 Aug 09, 2018 12:27 PM PDT 
Summer Graduate School Random and arithmetic structures in topology
Organizers: LEAD Alexander Furman (University of Illinois at Chicago), Tsachik 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 Apr 20, 2018 03:02 PM 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 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 Aug 03, 2018 11:17 AM 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 Aug 06, 2018 11:13 AM 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 Nov 06, 2018 10:39 AM PST 
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 Jan 10, 2019 09:13 AM PST 
Summer Graduate School Toric Varieties
Organizers: David Cox (Amherst College), Henry Schenck (Iowa State 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 Sep 21, 2018 04:02 PM 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 Feb 26, 2019 11:28 AM PST 
Summer Graduate School HPrinciple
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 Sep 21, 2018 04:02 PM PDT
Past Educational Events

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 Mar 08, 2019 01:46 PM PST 
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 
Workshop The 2018 Infinite Possibilities Conference
Organizers: Alejandra Alvarado (U.S. Navy), Hélène Barcelo (MSRI  Mathematical Sciences Research Institute), Rebecca Garcia (Sam Houston State University), Katharine Gurski (Howard University), LEAD Lily Khadjavi (Loyola Marymount University), Candice Price (University of San Diego), Kimberly Sellers (Georgetown University), Talitha Washington (Howard University), Kimberly Weems (North Carolina Central University), Ulrica Wilson (Morehouse College; Institute for Computational and Experimental Research in Mathematics (ICERM))The Infinite Possibilities Conference (IPC) is a national conference that is designed to promote, educate, encourage and support women of color interested in mathematics and statistics, as a step towards addressing the underrepresentation of AfricanAmericans, Latinas, Native Americans, and Pacific Islanders in these fields.
IPC aims to:
 fulfill a need for role models and communitybuilding
 provide greater access to information and resources for success in graduate school and beyond
 raise awareness of factors that can support or impede underrepresented women in the mathematical sciences
A unique gathering, the conference brings together participants from across the country, at all stages of education and career, for mentoring and mathematics.
Updated on May 18, 2018 12:18 PM PDT 
Workshop Latinx in the Mathematical Sciences Conference 2018
Organizers: Federico Ardila (San Francisco State University), Ricardo Cortez (Tulane University), Tatiana Toro (University of Washington), Mariel Vazquez (University of California, Davis)On March 810, 2018, IPAM will host a conference showcasing the achievements of Latinx in the mathematical sciences. The goal of the conference is to encourage Latinx to pursue careers in the mathematical sciences, to promote the advancement of Latinx currently in the discipline, to showcase research being conducted by Latinx at the forefront of their fields, and, finally, to build a community around shared academic interests. The conference will be held on the UCLA campus in Los Angeles, CA. It will begin at noon on Thursday, March 8.
This conference is sponsored by the Mathematical Sciences Institutes Diversity Initiative, with funding from the National Science Foundation Division of Mathematical Sciences.
Updated on Oct 23, 2017 04:53 PM PDT 
Workshop Critical Issues in Mathematics Education 2018: Access to mathematics by opening doors for students currently excluded from mathematics
Organizers: Aditya Adiredja (University of Arizona), LEAD Julia Aguirre (University of Washington  Tacoma), Kate Belin (Fannie Lou Hamer Freedom High School), LEAD Ricardo Cortez (Tulane University), Michael Driskill (Math for America ), Nicole Joseph (Vanderbilt University), Katherine Stevenson (California State University, Northridge), Francis Su (Harvey Mudd College), Maria del Rosario Zavala (San Francisco State University)Our mathematics education system is inequitable. It operates in ways that leave a significant proportion of students with negative mathematics experiences and inadequate mathematical preparation. The problem is historical and systemic, and the students most disaffected by the current system are overwhelmingly Black and Latino, Indigenous, poor, women, immigrant or first generation college students. If our mathematics community is to sustainably grow and thrive, mathematics education at all levels must be transformed.
This workshop focuses on students for whom we do not yet successfully ensure access to and advancement in mathematics. Sessions will share relevant programmatic efforts and innovative research that have been shown to maintain or increase students’ engagement and interests in mathematics across k12, undergraduate and graduate education. The sessions will focus particularly on reproducible efforts that affirm those students’ identities and their diverse intellectual resources and lived experiences. These efforts at various levels of mathematics education will highlight ways in which meaningful experiences in mathematics can disrupt ongoing systemic oppression. Participants will leave with conceptual and practical ways to open up and elevate mathematics education where all students thrive.
Updated on Jul 03, 2018 09:03 AM PDT 
Workshop Modern Math Workshop 2017
Organizers: Hélène Barcelo (MSRI  Mathematical Sciences Research 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))As part of the Mathematical Sciences Collaborative Diversity Initiatives, nine mathematics institutes are pleased to offer their annual SACNAS preconference event, the 2017 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. The Modern Math Workshop is part of the SACNAS National Conference; the workshop and the conference take place in the Salt Palace Convention Center in Salt Lake City, Utah. The MMW starts at 1:00 pm on Wednesday, October 18 with registration beginning at noon.
Updated on Oct 12, 2017 02:36 PM PDT 
Summer Graduate School Automorphic Forms and the Langlands Program
Organizers: LEAD Kevin Buzzard (Imperial College, London)The summer school will be an introduction to the more algebraic aspects of the theory of automorphic forms and representations. One of the goals will be to understand the statements of the main conjectures in the Langlands programme. Another will be to gain a good working understanding of the fundamental definitions in the theory, such as principal series representations, the Satake isomorphism, and of course automorphic forms and representations for groups such as GL_n and its inner forms.
Updated on Aug 04, 2017 11:02 AM PDT 
Summer Graduate School Nonlinear dispersive PDE, quantum many particle systems and the world between
Organizers: Natasa Pavlovic (University of Texas, Austin), Gigliola Staffilani (Massachusetts Institute of Technology), Nikolaos Tzirakis (University of Illinois at UrbanaChampaign)The purpose of the summer school is to introduce graduate students to the recent developments in the area of dispersive partial differential equations (PDE), which have received a great deal of attention from mathematicians, in part due to ubiquitous applications to nonlinear optics, water wave theory and plasma physics.
Recently remarkable progress has been made in understanding existence and uniqueness of solutions to nonlinear Schrodinger (NLS) and KdV equations, and properties of those solutions. We will outline the basic tools that were developed to address these questions. Also we will present some of recent results on derivation of NLS equations from quantum many particle systems and will discuss how methods developed to study the NLS can be relevant in the context of the derivation of this nonlinear equation.
Updated on Sep 12, 2017 02:02 PM PDT 
Summer Graduate School Séminaire de Mathématiques Supérieures 2017: Contemporary Dynamical Systems
Organizers: Sylvain Crovisier (Université de Paris VI (Pierre et Marie Curie)Université de Paris XI (ParisSud)), LEAD Konstantin Khanin (University of Toronto), Andrés Navas Flores (University of Santiago de Chile), Christiane Rousseau (Université de Montréal), Marcelo Viana (Institute of Pure and Applied Mathematics (IMPA)), Amie Wilkinson (University of Chicago)The theory of dynamical systems has witnessed very significant developments in the last decades, including the work of two 2014 Fields medalists, Artur Avila and Maryam Mirzakhani. The school will concentrate on the recent significant developments in the field of dynamical systems and present some of the present main streams of research. Two central themes will be those of partial hyperbolicity on one side, and rigidity, group actions and renormalization on the other side. Other themes will include homogeneous dynamics and geometry and dynamics on infinitely flat surfaces (both providing connections to the work of Maryam Mirzakhani), topological dynamics, thermodynamical formalism, singularities and bifurcations in analytic dynamical systems.
Updated on May 06, 2017 01:18 AM PDT 
Summer Graduate School Positivity Questions in Geometric Combinatorics
Organizers: Eran Nevo (The Hebrew University of Jerusalem), Raman Sanyal (Johann Wolfgang GoetheUniversität Frankfurt)McMullen’s gConjecture from 1970 is a shining example of mathematical foresight that combined all results available at that time to conjure a complete characterization of face numbers of convex simple/simplicial polytopes. The key statement in its verification is that certain combinatorial numbers associated to geometric (or topological) objects are nonnegative. The aim of this workshop is to introduce graduate students to selected contemporary topics in geometric combinatorics with an emphasis on positivity questions. It is fascinating that the dual notions of simple and simplicial polytopes lead to different but equally powerful algebraic frameworks to treat such questions. A key feature of the lectures will be the simultaneous development of these algebraic frameworks from complementary perspectives: combinatorialtopological and convexgeometric. General concepts (such as Lefschetz elements, Hodge–Riemann–Minkowski inequalities) will be developed sidebyside, and analogies will be drawn to concepts in algebraic geometry, Fourier analysis, rigidity theory and measure theory. This allows for entry points for students with varying backgrounds. The courses will be supplemented with guest lectures highlighting further connections to other fields.
Updated on Jul 21, 2017 10:13 AM PDT 
Summer Graduate School Soergel Bimodules
Organizers: LEAD Ben Elias (University of Oregon), Geordie Williamson (University of Sydney)We will give an introduction to categorical representation theory, focusing on the example of Soergel bimodules, which is a categorification of the IwahoriHecke algebra. We will give a comprehensive introduction to the "tool box" of modern (higher) representation theory: diagrammatics, homotopy categories, categorical diagonalization, module categories, Drinfeld center, algebraic Hodge theory.
Updated on Jul 10, 2017 01:18 PM PDT 
MSRIUP MSRIUP 2017: Solving Systems of Polynomial Equations
Organizers: LEAD Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI  Mathematical Sciences Research Institute), Herbert Medina (University of Portland), J. Maurice Rojas (Texas A & M University), 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 2017, MSRIUP will focus on Solving Systems of Polynomial Equations, a topic at the heart of almost every computational problem in the physical and life sciences. We will pay special attention to complexity issues, highlighting connections with tropical geometry, number theory, and the P vs. NP problem. The research program will be led by Prof. J. Maurice Rojas of Texas A&M University.Students who have had a linear algebra course and a course in which they have had to write proofs are eligible to apply. Due to funding restrictions, only U.S. citizens and permanent residents may apply regardless of funding. Members of underrepresented groups are especially encouraged to apply.Updated on Jun 28, 2018 05:38 PM PDT 
Summer Graduate School Subfactors: planar algebras, quantum symmetries, and random matrices
Organizers: LEAD Scott Morrison (Australian National University), Emily Peters (Loyola University), Noah Snyder (Indiana University)Subfactor theory is a subject from operator algebras, with many surprising connections to other areas of mathematics. This summer school will be devoted to understanding the representation theory of subfactors, with a particular emphasis on connections to quantum symmetries, fusion categories, planar algebras, and random matrices
Updated on Jun 20, 2017 03:34 PM PDT 
Workshop Career in Academia
Organizers: Hélène Barcelo (MSRI  Mathematical Sciences Research Institute), Estelle Basor (AIM  American Institute of Mathematics), David Farmer (AIM  American Institute of Mathematics), Sally Koutsoliotas (Bucknell University)This workshop will focus on preparing each participant for a successful career as a mathematician at a college or university. Beginning with the hiring process, a thorough discussion of the various elements of the application packet will take place in the context of each participant's materials. Working individually with experienced faculty, participants will review and refine their cover letters, C.V., research, and teaching statements. This will be followed by activities related to the interview. The primary goals of the workshop are to develop an understanding of the hiring process from the institutions' perspective, to refine the application packet, to learn what to expect during the interview process (including the job talk), and to prepare for negotiating salary and startup packages.
Additional time will be spent on aspects of the pretenure years including the development of a research program, writing grant proposals, and mentoring research students. The threeday workshop will consist of oneonone work with experienced mentors, small group discussions, critique of written materials, plenary sessions, and time for individual work and consultation.
Updated on May 06, 2017 01:18 AM PDT 
Summer Graduate School Commutative Algebra and Related Topics
Organizers: Shinobu Hikami (Okinawa Institute of Science and Technology), LEAD Shihoko Ishii (Tsinghua University), Kazuhiko Kurano (Meiji University), Kenichi Yoshida (Nihon University)The purpose of the school will be to introduce graduate students to foundational results in commutative algebra, with particular emphasis of the diversity of the related topics with commutative algebra. Some of these topics are developing remarkably in this decade and through learning those subjects the graduate students will be stimulated toward future research.
Updated on Jun 21, 2017 04:53 PM PDT 
Workshop Critical Issues in Mathematics Education 2017: Observing for Access, Power, and Participation in Mathematics Classrooms as a Strategy to Improve Mathematics Teaching and Learning
Organizers: Michael Driskill (Math for America ), Esther Enright (Boise State University), Rochelle Gutierrez (University of Illinois), LEAD Jodie Novak (University of Northern Colorado), LEAD Miriam Sherin (Northwestern University), Joi Spencer (University of San Diego), Elizabeth van Es (University of California, Irvine)Success rates in mathematics as well as recruitment and retention rates in the mathematics pipeline are low at all education levels and are, across predictable demographics, disproportionately low for students who are women, Latin@, Black, American Indian, recent immigrants, emergent bilinguals/multilinguals, and poor. Efforts to address these low rates often focus on programmatic solutions such as creating mentoring or bridge programs to address perceived deficiencies. While these programs achieve some success, evidence suggests that they may not substantially improve students’ subsequent success in mathematics or meaningfully address the ways that students experience mathematics instruction.
The 2017 CIME workshop will focus on observations of mathematics classrooms through the lens of equity. Specifically, we will use observation as a tool for understanding and improving imbalances of access, participation, and power in mathematics teaching and learning. In doing so, we seek to better understand students’ experiences in mathematics classrooms in order to improve academic success, recruitment and retention, and meaningful experiences for historically marginalized populations.
Five questions structure the highly interactive design of the workshop:
 What does it mean to create an equitable classroom environment? How can the structure of classroom interactions lead to imbalances of access, identity, and power in mathematics teaching and learning? How can such structures be rebuilt to better serve all students?
 How might observations of mathematics instruction help us to identify power dynamics in classrooms? What language is helpful to describe interactions in mathematics classrooms? What might we learn from observations about how culture and identity are developed for some students but not others? What do classroom observations reveal about how instruction supports or discourages engagement in mathematics for students of different backgrounds?
 What does it mean to observe interactions in a mathematics classroom with an eye towards equity? What language is helpful to describe interactions in mathematics classrooms? How do we observe and describe interactions among students, between students and mathematics, between students and instructors, and between students and resources (i.e., textbooks, computers, chalkboards, manipulatives)?
 What professional experiences can support mathematics instructors to learn how to observe for, describe, interpret, and productively address interactions in the mathematics classroom from the lens of equity? What professional experiences can support mathematics instructors to increase the number of equitable interactions and decrease the number of inequitable ones in their classrooms?
 What measures might be useful in tracking our progress in learning to see, describe, interpret, and productively address (in)equitable interactions in mathematics classrooms? What measures and tools might be useful in tracking the impacts on instruction and student learning? How might we develop infrastructure to help with this work (video library, faculty resources, etc.)?
Updated on May 06, 2017 01:18 AM PDT