
Summer Graduate School Commutative Algebra and its Interaction with Algebraic Geometry (Notre Dame)
Organizers: Steven Cutkosky (University of Missouri), LEAD Claudia Polini (University of Notre Dame), Claudiu Raicu (University of Notre Dame), Steven Sam (University of California, San Diego), Kevin Tucker (University of Illinois at Chicago)Commutative Algebra has seen an extraordinary development in the last few years. Long standing conjectures have been proven and new connections to different areas of mathematics have been built.This summer graduate school will consist of three minicourses (5 lectures each) on fundamental topics in commutative algebra that are not covered in the standard courses. Each course will be accompanied by problem sessions focused on research. Five general colloquiumstyle lectures will be given by invited scholars who will also attend the school and help with afternoon research activities.
Updated on Mar 20, 2023 01:33 PM PDT

Summer Graduate School Formalization of Mathematics (SLMath)
Organizers: Jeremy Avigad (Carnegie Mellon University), Heather Macbeth (Fordham University at Lincoln Center), Patrick Massot (Université ParisSaclay)Computational proof assistants now make it possible to develop global, digital mathematical libraries with theorems that are fully checked by computer. This summer school will introduce students to the new technology and the ideas behind it, and will encourage them to think about the goals and benefits of formalized mathematics. Students will learn to use the Lean interactive proof assistant, and by the end of the session they will be in a position to formalize mathematics on their own, join the Lean community, and contribute to its mathematical library.
Updated on May 11, 2023 02:03 PM PDT 
MSRIUP MSRIUP 2023: Topological Data Analysis
Organizers: Federico Ardila (San Francisco State University), LEAD Maria Mercedes Franco (Queensborough Community College (CUNY)), Rebecca Garcia (Sam Houston State University), Jose Perea (Northeastern University), Candice Price (Smith College), Robin Wilson (Loyola Marymount University)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 2023, MSRIUP will focus on Topological Data Analysis. The research program will be led by Dr. Jose Perea, Associate Professor in the Department of Mathematics and the Khoury College of Computer Sciences at Northeastern University.
Updated on Mar 20, 2023 08:50 AM PDT 
Summer Graduate School Algebraic Methods for Biochemical Reaction Networks (Leipzig, Germany)
Organizers: Timo de Wolff (TU Braunschweig), LEAD Alicia Dickenstein (University of Buenos Aires), Elisenda Feliu (University of Copenhagen)The aim of the course is to learn how tools from algebraic geometry (in particular, from computational and real algebraic geometry) can be used to analyze standard models in molecular biology. Particularly, these models are key ingredients in the development of Systems and Synthetic biology, two active research areas focusing on understanding, modifying, and implementing the design principles of living systems.
We will focus on the mathematical aspects of the methods, and exemplify and apply the theory to real networks, thereby introducing the participants to relevant problems and mechanisms in molecular biology. As a counterpart, however, the participants will also see how this field has in the past challenged current methods, mainly in the realm of real algebraic geometry, and has given rise to new general and purely theoretical results on polynomial equations. We will end our lectures with an overview of open questions in both fields.
Updated on Apr 24, 2023 03:46 PM PDT 
Summer Graduate School Séminaire de Mathématiques Supérieures 2023: Periodic and Ergodic Spectral Problems (Montréal, Canada)
Organizers: Alexander Elgart (Virginia Polytechnic Institute and State University), Vojkan Jaksic (McGill University), Svetlana Jitomirskaya (University of California, Irvine), Ilya Kachkovskiy (Michigan State University), Jean Lagacé (King's College London), Leonid Parnovski (University College London)This two week school will focus on spectral theory of periodic, almostperiodic, and random operators. The main aim of this school is to teach the students who work in one of these areas, methods used in parallel problems, explain the similarities between all these areas and show them the `big picture'.
Updated on Apr 06, 2023 06:24 PM PDT 
Summer Graduate School Mathematics and Computer Science of Market and Mechanism Design (SLMath)
Organizers: Yannai Gonczarowski (Harvard University), Irene Lo (Stanford University), Ran Shorrer (Pennsylvania State University), LEAD Inbal TalgamCohen (TechnionIsrael Institute of Technology)This school is associated with an upcoming research program at MSRI under the same title. The goal of the school is to equip students unfamiliar with these topics with the mathematical and theoretical computer science toolbox that forms the foundation of market and mechanism design.
Updated on May 11, 2023 12:37 PM PDT 
Summer Graduate School Topics in Geometric Flows and Minimal Surfaces (St. Mary's College)
Organizers: Ailana Fraser (University of British Columbia), LanHsuan Huang (University of Connecticut), Catherine Searle (Wichita State University), Lu Wang (Yale University)This graduate summer school will introduce students to two important and interrelated fields of differential geometry: geometric flows and minimal surfaces.
Geometric flows have had far reaching influences on numerous branches of mathematics and other scientific disciplines. An outstanding example is the completion of Hamilton’s Ricci flow program by Perelman, leading to the resolution of the Poincare conjecture and Thurston’s geometrization conjecture for 3manifolds. In this part of the summer school, students will be guided through basic topics and ideas in the study of geometric flows.
Since Penrose used variations of volume to formulate and study black holes in general relativity (in his Nobel prizewinning work), the intriguing connections between minimal surfaces and general relativity have been a strong driving force for the modern developments of both research areas. This part of the summer school will introduce students to the basic theory of minimal submanifolds and its applications in Riemannian geometry and general relativity.
The curriculum of this program will be accessible and will have a broad appeal to graduate students from a variety of mathematical areas, introducing some of the latest developments in each area and the remaining open problems therein, while simultaneously emphasizing their synergy.
Updated on Apr 27, 2023 12:13 PM PDT 
Summer Graduate School Machine Learning (UC San Diego)
Organizers: Ery AriasCastro (University of California, San Diego), Mikhail Belkin (University of California, San Diego), Yusu Wang (Univ. California, San Diego), Lily Weng (University of California, San Diego)The overarching goal of this summer school is to expose the students both to modern forms of unsupervised learning — in the form of geometrical and topological data analysis — and to supervised learning — in the form of (deep) neural networks applied to regression/classification problems. The organizers have opted for a lighter exposure to a broader range of topics. Using the metaphor of a meal, we are offering 2 + 2 samplers — geometry and topology for data analysis + theoretical and practical deep learning — rather than 1 + 1 main dishes. The main goal, thus, is to inspire the students to learn more about one or several of the topics covered in the school.
The expected learning outcomes for students attending the school are the following:
1. An introduction to how concepts and tools from geometry and topology can be leveraged to perform data analysis in situations where the data are not labeled.
2. An introduction to recent and ongoing theoretical and methodological/practical developments in the use of neural networks for data analysis (deep learning).
Updated on Mar 19, 2023 06:44 PM PDT 
Summer Graduate School Introduction to Derived Algebraic Geometry (UC Berkeley)
Organizers: Benjamin Antieau (Northwestern University), Dmytro Arinkin (University of WisconsinMadison)Derived algebraic geometry is an ‘update’ of algebraic geometry using ‘derived’ (roughly speaking, homological) techniques. This requires recasting the very foundations of the field: rings have to be replaced by differential graded algebras (or other forms of derived rings), categories by higher categories, and so on. The result is a powerful set of new tools, useful both within algebraic geometry and in related areas. The school serves as an introduction to these techniques, focusing on their applications.
The school is built around two related courses on geometric (‘derived spaces’) and categorical (‘derived categories’) aspects of the theory. Our goal is to explain the key ideas and concepts, while trying to keep technicalities to a minimum.
Updated on May 17, 2023 04:21 PM PDT 
Summer Graduate School Concentration Inequalities and Localization Techniques in High Dimensional Probability and Geometry (SLMath)
Organizers: Max Fathi (Université Paris Cité), Dan Mikulincer (Massachusetts Institute of Technology)The goal of the summer school is for the students to first become familiar with the concept of concentration of measure in different settings (Euclidean, Riemannian and discrete), and the main open problems surrounding it. The students will later become familiar with the proof techniques that involve the different types of localization and obtain expertise on the ways to apply the localization techniques. After attending the graduate school, the students are expected to have the necessary background that would give them a chance to both conduct research around open problems in concentration of measure, find new applications to existing localization techniques and perhaps also develop new localization techniques.
Updated on Mar 13, 2023 11:34 AM PDT 
Summer Graduate School Mathematics of Big Data: Sketching and (Multi) Linear Algebra (IBM Almaden)
Organizers: Kenneth Clarkson (IBM Research Division), Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University), Tamara Kolda (MathSci.ai), Shashanka Ubaru (IBM Thomas J. Watson Research Center)This summer school will introduce graduate students to sketchingbased approaches to computational linear and multilinear algebra. Sketching here refers to a set of techniques for compressing a matrix, to one with fewer rows, or columns, or entries, usually via various kinds of random linear maps. We will discuss matrix computations, tensor algebras, and such sketching techniques, together with their applications and analysis.
Updated on Nov 03, 2022 11:59 AM PDT 
Summer Graduate School Foundations and Frontiers of Probabilistic Proofs (Zürich, Switzerland)
Organizers: Alessandro Chiesa (École Polytechnique Fédérale de Lausanne (EPFL))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 Apr 18, 2023 02:28 PM PDT 
Workshop Hot Topics: MIP* = RE and the Connes’ Embedding Problem
Organizers: Michael Chapman (New York University, Courant Institute), Anand Natarajan (Massachusetts Institute of Technology), William Slofstra (University of Waterloo), John Wright (University of Texas, Austin), Henry Yuen (Columbia University)This workshop is about the recent MIP*=RE result from quantum computational complexity, and the resulting resolution of the Connes embedding problem from the theory of von Neumann algebras. MIP*=RE connects the disparate areas of computational complexity theory, quantum information, operator algebras, and approximate representation theory. The aim of this workshop is to bridge this divide, by giving an indepth exposition of the techniques used in the proof of MIP*=RE, and highlighting perspectives on the MIP*=RE result from operator algebras and approximate representation theory. In particular, this workshop will highlight connections with group stability, something that has not been covered in previous workshops. In addition to increasing understanding of the MIP*=RE proof, we hope that this will open up further applications of the ideas behind MIP*=RE in operator algebras.
Updated on Mar 30, 2023 04:00 PM PDT 
Summer Graduate School Stochastic Quantization
Organizers: Massimiliano Gubinelli (Rheinische FriedrichWilhelmsUniversität Bonn), Martina Hofmanova (Universität Bielefeld), LEAD Hao Shen (University of WisconsinMadison), Lorenzo Zambotti (Université de Paris VI (Pierre et Marie Curie))This summer school will familiarize students with the basic problems of the mathematical theory of Euclidean quantum fields. The lectures will introduce some of its prominent models and analyze them via the so called “stochastic quantization” methods, involving recently developed stochastic and PDE techniques. This is an area which is highly interdisciplinary combining ideas ranging from the theory of partial differential equations, to stochastic analysis, to mathematical physics. Our goal is to bring together students which are maybe familiar with some but not all of these subjects and teach them how to integrate these different tools to solve cuttingedge problems of Euclidean quantum field theory.
Updated on May 24, 2023 11:54 AM PDT
Past Educational Events

MSRIUP Mathematically Advancing Young Undergraduates Program (MAYUP) [2023 Pilot Program]
Organizers: Duane Cooper (Morehouse College), Shelby Wilson (Morehouse College; Johns Hopkins University Applied Physics Lab)2023 Pilot Program: The goal of MAYUP is to provide students with a glimpse into Linear Algebra; and the ways in which this topic may arise both theoretically and computationally in their future studies. Material will include an introduction to matrices as well as basic matrix operations. We will also provide students with introductory programming skills in Python, including development environment setup and matrix manipulations via code.
Updated on Feb 23, 2023 04:27 PM PST 
Workshop May 12, a Celebration for Women in Mathematics (2023)
Organizers: Ini Adinya (University of Ibadan), Masha Albrecht (Berkeley High School), Romina Arroyo (Universidad Nacional de Cordoba), MariaGrazia Ascenzi (University of California Los Angeles), Mirela Ciperiani (University of Texas, Austin), Donatella Danielli (Arizona State University), Shanna Dobson (University of California, Riverside), Malena Espanol (Arizona State University), Olubunmi FadipeJoseph (University of Ilorin), Anna Fino (Università di Torino), Natalia GarciaFritz (Pontificia Universidad Católica de Chile), Adi Glucksam (Northwestern University), M.E. Hogan (Texas Tech University), KueiNuan Lin (Pennsylvania State University), Zheng Liu (University of California, Santa Barbara), Liangbing Luo (Lehigh University), LEAD Ornella Mattei (San Francisco State University), Julia Plavnik (Indiana University), Palina Salanevich (Universiteit Utrecht), Ramdorai Sujatha (University of British Columbia)The Simons Laufer Mathematical Sciences Institute (SLMath), formerly MSRI, celebrates May 12 with a panel discussion and social event open to all on the topic "Pathways in Mathematics". This is a hybrid event taking place on Zoom and in person at SLMath and satellite institutions.
Updated on May 17, 2023 02:43 PM PDT 
Workshop MSRI / SLMath 40th Anniversary Symposium
Organizers: Hélène Barcelo (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath)), Charles Fefferman (Princeton University), Dan Freed (University of Texas, Austin), Kristin Lauter (Facebook AI Research (FAIR) North America at Meta), Dusa McDuff (Barnard College), Andrei Okounkov (Columbia University; University of California, Berkeley), Tatiana Toro (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath))In 202223, SLMath (formerly MSRI) celebrates 40 years of serving the mathematical sciences community through our topicfocused programs and workshops, and the general public via our national and global outreach initiatives. Director Tatiana Toro and Deputy Director Hélène Barcelo invite the community to join us for a symposium to reflect upon these four decades of extraordinary activity. This celebration will feature special guest speakers, panel discussions and an evening reception.
This event is free and open to the public. To register, log into MSRI.org or create an account. Funding for attendance is extremely limited. Click below to expand the event description and schedule.
Updated on May 15, 2023 01:23 PM PDT 
Workshop Critical Issues in Mathematics Education 2023: Mentoring for Equity
Organizers: Pamela Harris (University of WisconsinMilwaukee), Abbe Herzig (TPSEMath), LEAD Aris Winger (Georgia Gwinnett College), Michael Young (Carnegie Mellon University)The workshop Critical Issues in Mathematics Education: Mentoring for Equity aims to reach a broad audience of faculty and students in postsecondary mathematical sciences. Participants will learn about the evidence base for effective mentoring, with a focus on culturally responsive mentoring that supports all students and faculty along their mathematical paths. The workshop includes a combination of discussion of research evidence, review and adaptation of practical tools, and explicit training in effective mentoring, including how to bring these tools back to participants’ home institutions. The workshop intertwines objectives of increasing participants’ knowledge of the scholarship on effective mentoring, and engages participants in interactive activities to develop tangible skills as mentors and as mentortrainers. Participants should come with a growth mindset, prepared to reflect on their experiences as mentors and mentees, and actively contribute to activities that build skills for implementing best mentoring practices. This workshop will cultivate local and national mentoring communities that bring effective tools and strategies to mentoring, so that mentees can persist and thrive in research, teaching, education, and throughout their education and careers. One focus will be on addressing the individual mentoring needs of all faculty and students, including those who have been historicallymarginalized in mathematics education and careers.
Updated on Mar 30, 2023 01:00 PM PDT 
Workshop Modern Math Workshop 2022
Organizers: Hélène Barcelo (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath)), Philip Hammer (Institute for Mathematical and Statistical Innovation), 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))ALL FUNDING FOR THIS WORKSHOP HAS BEEN ALLOCATED
As part of the Mathematical Sciences Collaborative Diversity Initiatives, the six NSFfunded U.S. mathematics institutes will host their annual SACNAS preconference event, the 2022 Modern Math Workshop (MMW). The Modern Math Workshop encourages undergraduates from underrepresented groups to pursue careers in the mathematical sciences, and builds research and networking opportunities among undergraduates, graduate students and recent PhDs.
Updated on Nov 29, 2022 08:49 AM PST 
Summer Graduate School Sums of Squares Method in Geometry, Combinatorics and Optimization (BIRS)
Organizers: LEAD Grigoriy Blekherman (Georgia Institute of Technology), Annie Raymond (University of Massachusetts Amherst), Cynthia Vinzant (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 Apr 07, 2022 02:41 PM PDT 
Summer Graduate School Tropical Geometry
Organizers: Renzo Cavalieri (Colorado State University), Hannah Markwig (EberhardKarlsUniversität Tübingen), Dhruv Ranganathan (University of Cambridge)Enumerative geometry and the theory of moduli spaces of curves are two cornerstones of modern algebraic geometry; the two subjects have had a significant influence on each other. In the last 15 years, discrete and combinatorial methods, systematized within tropical geometry, have begun to provide new avenues of access into these two subjects. The goal of this summer school is to give students crash courses in tropical and logarithmic geometry, with a particular focus on the applications in enumerative geometry and moduli theory. The school will consist of three courses of seven lectures each:
 Enumeration of tropical curves/ by Hannah Markwig
 Curve counting in tropical and algebraic geometry by Renzo Cavalieri
 Logarithmic geometry and stable map/s by Dhruv Ranganathan
Updated on Aug 12, 2022 03:03 PM PDT 
Summer Graduate School Mathematics of Machine Learning (INdAM and Courant Institute)
Organizers: Sebastien Bubeck (Microsoft Research)This school is offered in partnership with Istituto Nazionale di Alta Matematica (INdAM) and the Courant Institute of Mathematical Sciences.
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 12, 2022 11:42 AM PDT 
Summer Graduate School Topological Methods for the Discrete Mathematician
Organizers: Pavle Blagojevic (Freie Universität Berlin), Florian Frick (Carnegie Mellon University), Shira Zerbib (Iowa State University)Recently, progress in the field of topological methods in discrete mathematics has been rapid and has generated a lot of activity with the resolution of major open problems, the emergence of new lines of inquiry, and the development of new tools. These exciting new developments have not been digested into a textbook treatment. The two main goals of this school are to:
 Provide graduate students with a thorough introduction to novel topological techniques and to a handful of their applications in the fields of combinatorics and discrete geometry with short glimpses into mathematical mechanics and algorithm complexity.
 Expose students to current research, and guide them in research on open problems in discrete mathematics using modern topological tools.
The summer school will lead participants from appealing, simpletostate problems at confluence of combinatorics, geometry, and topology to sophisticated topological methods that are required for their resolution. In recent years topological methods have found numerous novel applications in mathematics and beyond, such as in data science, machine learning, economics, the social sciences, and biology. The problems we will discuss are particularly wellsuited to rapidly put students in a position to approach related research questions.
Updated on Feb 14, 2023 01:39 PM PST 
Summer Graduate School MSRINCTS Joint Summer School: Recent Topics in Well Posedness
Organizers: Jungkai Chen (National Taiwan University), Mimi Dai (University of Illinois at Chicago), Yoshikazu Giga (University of Tokyo), Tsuyoshi Yoneda (Hitotsubashi University)This school is offered in partnership with the National Center for Theoretical Sciences.
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 12, 2022 11:40 AM PDT 
Summer Graduate School 2022 Joint PCMI School: Number Theory Informed by Computation
Organizers: Jennifer Balakrishnan (Boston University), Rafe Mazzeo (Stanford University), Bjorn Poonen (Massachusetts Institute of Technology), Akshay Venkatesh (Institute for Advanced Study)The PCMI graduate summer school program in 2022 will consist of a sequence of 11 minicourses. The lecturers and topics for these minicourses are listed below. Each minicourse is accompanied by a problem session. The topics are arranged so that there is good material and opportunities for learning both for less experienced students as well as more advanced students. Beyond their attendance in these minicourse sessions, all graduate participants will be able to take part in the substantial other benefits of a PCMI session. This includes the opportunity to interact with the researchers in residence and take part in the research seminar component of PCMI. Many graduate students also interact in significant ways with the undergraduate cohort,,the undergraduate faculty cohort, and may also participate in the many pedagogically focused activities which form part of the K12 Teacher Leadership Program and the Workshop for Equity in Mathematics Education. PCMI includes numerous crossprogram activities to help members from all these groups interact with one another.
Updated on Feb 02, 2022 03:52 PM PST 
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 Feb 14, 2022 12:29 PM PST 
Summer Graduate School Séminaire de Mathématiques Supérieures 2022: Floer Homotopy Theory
Organizers: Kristen Hendricks (Rutgers University), Ailsa Keating (University of Cambridge), Robert Lipshitz (University of Oregon), Liam Watson (University of British Columbia), Ben Williams (University of British Columbia)The idea of stable homotopy refinements of Floer homology was first introduced by Cohen, Jones, and Segal in a 1994 paper, but it was only in the last decade that this idea became a key tool in lowdimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)equivariant SeibergWitten Floer homotopy type to resolve the Triangulation Conjecture and AbouzaidBlumberg's use of Floer homotopy theory and Morava Ktheory to prove the general Arnol'd Conjecture in finite characteristic. During this period, a range of related techniques, included under the umbrella of Floer homotopy theory, have also led to important advances, including involutive Heegaard Floer homology, Smith theory for Lagrangian intersections, homotopy coherence, and further connections between string topology and Floer theory. These in turn have sparked developments in algebraic topology, ranging from developments on Lie algebras in derived algebraic geometry to new computations of equivariant Mahowald invariants to new results on topological Hochschild homology.
The goal of the summer school is to provide participants the tools in symplectic geometry and stable homotopy theory required to work on Floer homotopy theory. Students will come away with a basic understanding of some of the key techniques, questions, and challenges in both of these fields. The summer school may be particularly valuable for participants with a solid understanding of one of the two fields who want to learn more about the other and the connections between them.Updated on May 27, 2022 09:41 AM 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 14, 2022 09:37 AM PDT 
Summer Graduate School Algebraic Theory of Differential and Difference Equations, Model Theory and their Applications
Organizers: LEAD Alexey Ovchinnikov (Queens College, CUNY), Anand Pillay (University of Notre Dame), Thomas Scanlon (University of California, Berkeley)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 Jan 11, 2023 02:38 PM PST 
Seminar ADJOINT Professional Development Panel  Work, Wellness & Autonomy
Updated on Jun 22, 2022 01:56 PM PDT 
Summer Graduate School New Directions in Representation Theory (AMSI and U. of Hawaii, Hilo)
Organizers: Angela Coughlin (Australian Mathematical Sciences Institute), Joseph Grotowski (University of Queensland), Tim Marchant (Australian Mathematical Sciences Institute), Ole Warnaar (University of Queensland), Geordie Williamson (University of Sydney)This school is offered in partnership with the Australian Mathematical Sciences Institute and the University of Hawaii, Hilo.
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 12, 2022 11:38 AM PDT 
Summer Graduate School Geometric Flows (Crete, 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 collaboration 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. Information about the location of the summer school can be found here.
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 Sep 30, 2022 12:18 PM PDT 
MSRIUP MSRIUP 2022: Algebraic Methods in Mathematical Biology
Organizers: LEAD Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Mercedes Franco (Queensborough Community College (CUNY)), Rebecca Garcia (Sam Houston State University), Candice Price (Smith College), Anne Shiu (Texas A & M University; Texas A&M University)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 2022, MSRIUP will focus on Algebraic Methods in Mathematical Biology. The research program will be led by Dr. Anne Shiu, Associate Professor of Mathematics at Texas A&M University.
Updated on Mar 17, 2023 02:38 PM PDT 
Summer Graduate School Integral Equations and Applications
Organizers: Fioralba Cakoni (Rutgers University), Dorina Mitrea (Baylor University), Irina Mitrea (Temple University), Shari Moskow (Drexel University)The field of Integral Equations has a long and distinguished history, being the driving force behind many fundamental developments in various areas of mathematics including Harmonic Analysis, Partial Differential Equations, Potential Theory, Scattering Theory, Functional Analysis, Complex Analysis, Operator Theory, Mathematical Physics and Numerical Analysis.
This school will:
 introduce graduate students to the systematic study of integral equations;
 present some of the latest theoretical advancements in the field and open problems; and
 involve participants in a handson discovery lab focused on deriving results about integral operators in two dimensions relevant for both the theoretical and numerical treatment of Integral Equations in two dimensions. The curriculum of this program will be accessible and will have a broad appeal to graduate students from a variety of mathematical areas (both theoretical and applied).
Updated on Aug 11, 2022 09:23 AM PDT 
Workshop May 12, a Celebration for Women in Mathematics, year 2022
Organizers: Ini Adinya (University of Ibadan), MariaGrazia Ascenzi (University of California Los Angeles), Hajer Bahouri (Laboratoire JacquesLouis Lions; Centre National de la Recherche Scientifique (CNRS)), Hélène Barcelo (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath)), Lenore Blum (University of California, Berkeley; Carnegie Mellon University), Donatella Danielli (Arizona State University), Shanna Dobson (University of California, Riverside), Malena Espanol (Arizona State University), Vasiliki Evdoridou (The Open University), Olubunmi FadipeJoseph (University of Ilorin), Anna Fino (Università di Torino), Adi Glucksam (Northwestern University), Eriko Hironaka (Florida State University), M.E. Hogan (Texas Tech University), Kyounghee Kim (Florida State University), KueiNuan Lin (Pennsylvania State University), Liangbing Luo (Lehigh University), LEAD Ornella Mattei (San Francisco State University), Betul OrcanEkmekci (Rice University), Leticia Pardo Simon (University of Manchester), Julia Plavnik (Indiana University), Palina Salanevich (Universiteit Utrecht), Awais Shaukat (Government College University Lahore), Tara Taylor (St. Francis Xavier University)MSRI's 2022 Celebration of Women in Math event will be for graduate students, with a focus on "How to build a Career in Math". It will be a hybrid workshop, with online and inperson activities at satellite institutions.
The event will include a panel discussion, social activities, and breakout sessions on the following topics:
 Finding (having) mentors
 How to build a network and collaborations
 How to become an independent researcher
 How to balance teaching/research/admin/life
Registration is open.
Updated on May 26, 2022 02:41 PM PDT 
Workshop [Hybrid Workshop] Critical Issues in Mathematics Education 2022: Initiating, Sustaining, and Researching Mathematics Department Transformation of Introductory Courses for STEM Majors
Organizers: Naneh Apkarian (Arizona State University), David Bressoud (Macalester College), Pamela Burdman (Just Equations), Jamylle Carter (Diablo Valley college), Ted Coe (Northwest Evaluation Association), Courtney Ginsberg (Math for America), Estrella Johnson (Virginia Polytechnic Institute and State University), W Gary Martin (Auburn University), Michael O'Sullivan (San Diego State University), LEAD Chris Rasmussen (San Diego State University), Daniel Reinholz (San Diego State University), Wendy Smith (University of Nebraska), David Webb (University of Colorado at Boulder)The world is changing, along with perceptions. Many call for the improvement of mathematics teaching and learning, for both citizenry and STEM preparation. To achieve sustainable change, though, the focus needs to extend from individuals to systems. It is not enough to change one classroom or one course. Transformation requires change at all levels: in teaching, programmatic practices, and institutions. This workshop will bring together teachers and researchers from universities, community colleges, and K12 schools to explore the reasons for and processes by which change in university mathematics departments is initiated, promoted, and sustained and lessons learned from change efforts in K12. It will review what we know about change at all levels and reflect on stories of failure and success.
Updated on Mar 14, 2022 12:02 PM PDT 
Workshop Blackwell Tapia Conference 2021
Organizers: David Banks (Duke University), Hélène Barcelo (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath)), Lloyd Douglas, Robert Megginson (University of Michigan), Mariel Vazquez (University of California, Davis), Ulrica Wilson (Morehouse College; Institute for Computational and Experimental Research in Mathematics (ICERM))MSRI and the Mathematical Science Institutes Diversity Initiative (MSIDI) are pleased to announce that the 2021 BlackwellTapia Conference (rescheduled from Fall 2020), will be held simultaneously at four locations nationwide. The conference will celebrate the 2020 BlackwellTapia prize winner, Tatiana Toro (University of Washington), who has recently been announced as the next Director of MSRI, effective August 2022.
ONLY REGISTRATIONS FOR VIRTUAL PARTICIPATION ARE BEING ACCEPTED AS OF NOVEMBER 8.
Choose from four host sites nationwide:
Mathematical Sciences Research Institute (MSRI): Berkeley, California
Institute for Pure and Applied Mathematics (IPAM): Los Angeles, California
Institute for Mathematical and Statistical Innovation (IMSI): Chicago, Illinois
Institute for Advanced Study (IAS): Princeton, New JerseyUpdated on Nov 08, 2021 10:30 AM PST 
Summer Graduate School Foundations and Frontiers of Probabilistic Proofs (Virtual School)
Organizers: Alessandro Chiesa (École Polytechnique Fédérale de Lausanne (EPFL)), 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 Aug 11, 2021 12:27 PM PDT 
Summer Graduate School Random Conformal Geometry (Virtual School)
Organizers: Mario Bonk (University of California, Los Angeles), Steffen Rohde (University of Washington), LEAD Fredrik Viklund (Royal Institute of Technology)This Summer Graduate School will cover basic tools that are instrumental in Random Conformal Geometry (the investigation of analytic and geometric objects that arise from natural probabilistic constructions, often motivated by models in mathematical physics) and are at the foundation of the subsequent semesterlong program "The Analysis and Geometry of Random Spaces". Specific topics are Conformal Field Theory, Brownian Loops and related processes, Quasiconformal Maps, as well as Loewner Energy and Teichmüller Theory.
Updated on Mar 19, 2021 03:03 PM PDT 
Summer Graduate School Gauge Theory in Geometry and Topology (Virtual School)
Organizers: Lynn Heller (Universität Hannover), Francesco Lin (Columbia University), LEAD Laura Starkston (University of California, Davis), Boyu Zhang (University of Maryland)Figure 1. A rotationally symmetric solution to the selfduality equations on an open and dense subset of the torus. Singularities appear where the surface intersects the ideal boundary at infinity of the hyperbolic 3space visualized by the wireframe.
Gauge theory is a geometric language used to formulate many fundamental physical phenomena, which has also had profound impact on our understanding of topology. The main idea is to study the space of solutions to partial differential equations admitting a very large group of local symmetries. Starting in the late 1970s, mathematicians began to unravel surprising connections between gauge theory and many aspects of geometric analysis, algebraic geometry and lowdimensional topology. This influence of gauge theory in geometry and topology is pervasive nowadays, and new developments continue to emerge.
The goal of the summer school is to introduce students to the foundational aspects of gauge theory, and explore their relations to geometric analysis and lowdimensional topology. By the end of the twoweek program, the students will understand the relevant analytic and geometric aspects of several partial differential equations of current interest (including the YangMills ASD equations, the SeibergWitten equations, and the Hitchin equations) and some of their most impactful applications to problems in geometry and topology.
Updated on Jun 28, 2021 12:06 PM PDT