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  1. Workshop Modern Math Workshop 2022

    Organizers: Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), 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 NSF-funded U.S. mathematics institutes will host their annual SACNAS pre-conference 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 Sep 13, 2022 12:28 PM PDT
  2. Workshop Critical Issues in Mathematics Education 2023: Mentoring for Equity

    Organizers: Pamela Harris (University of Wisconsin-Milwaukee), Abbe Herzig (AHH Consulting), 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 mentor-trainers. 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 historically-marginalized in mathematics education and careers.

    Updated on Jul 27, 2022 02:12 PM PDT
  3. Workshop MIP* = RE and the Connes’ Embedding Problem

    Organizers: Michael Chapman (Hebrew University), 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 in-depth 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 Sep 22, 2022 08:51 AM PDT
  4. 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)
    1015 image

    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 mini-courses (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 colloquium-style lectures will be given by invited scholars who will also attend the school and help with afternoon research activities. 

    Updated on Sep 26, 2022 12:06 PM PDT
  5. Summer Graduate School Formalization of Mathematics

    Organizers: Jeremy Avigad (Carnegie Mellon University), Heather Macbeth (Fordham University at Lincoln Center), Patrick Massot (Université Paris-Saclay)
    Image
    Some basic concepts in mathlib and the dependencies between them

    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 Sep 26, 2022 09:18 AM PDT
  6. MSRI-UP MSRI-UP 2023: Topological Data Analysis

    Organizers: Federico Ardila (San Francisco State University), LEAD Maria Franco (Queensborough Community College (CUNY); MSRI - Mathematical Sciences Research Institute), Rebecca Garcia (Sam Houston State University), Jose Perea (Michigan State University), Candice Price (Smith College), Robin Wilson (California State Polytechnic University, Pomona)

    The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

    In 2023, MSRI-UP 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 Sep 09, 2022 03:36 PM PDT
  7. Summer Graduate School Machine Learning (UCSD)

    Organizers: Ery Arias-Castro, 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 Sep 26, 2022 02:47 PM PDT
  8. Summer Graduate School Algebraic Methods for Biochemical Reaction Networks (Leipzig, Germany)

    Organizers: Timo de Wolff (TU Berlin), LEAD Alicia Dickenstein (University of Buenos Aires), Elisenda Feliu (University of Copenhagen)
    2021 sgs biochemical reaction networks leipzig image dickenstein.2019.10.09 %281%29
    A basic enzymatic mechanism

    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 Sep 23, 2022 03:41 PM PDT
  9. Summer Graduate School Séminaire de Mathématiques Supérieures 2023: Periodic and Ergodic Spectral Problems

    Organizers: David Damanik (Rice University), Alexander Elgart (Virginia Polytechnic Institute and State University), Vojkan Jaksic (McGill University), Svetlana Jitomirskaya (University of California, Irvine), Jean Lagacé (University College London), Iosif Polterovich (Université de Montréal)

    This two week school will focus on spectral theory of periodic, almost-periodic, 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 Sep 26, 2022 01:54 PM PDT
  10. Summer Graduate School Mathematics and Computer Science of Market and Mechanism Design

    Organizers: Yannai Gonczarowski (Microsoft Research), Irene Yuan Lo (Stanford University), Ran Shorrer (Pennsylvania State University), LEAD Inbal Talgam-Cohen (Technion---Israel 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 Sep 23, 2022 05:05 PM PDT
  11. Summer Graduate School Topics in Geometric Flows and Minimal Surfaces

    Organizers: Ailana Fraser (University of British Columbia), Lan-Hsuan Huang (University of Connecticut), Catherine Searle (Wichita State University), Lu Wang (Yale University)
    Bubble
    Soap bubble: equilibrium solution of the rescaled mean curvature flow and constant curvature surface.

    This graduate summer school will introduce students to two important and inter-related 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 3-manifolds. 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 prize-winning 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 Sep 26, 2022 12:27 PM PDT
  12. Summer Graduate School Introduction to Derived Algebraic Geometry

    Organizers: Benjamin Antieau (Northwestern University), Dmytro Arinkin (University of Wisconsin-Madison)
    Image
    Schur quartic x 4−xy3 = z 4−zu3 and several of the 64 lines that it contains

    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 Sep 27, 2022 10:10 AM PDT

Past Educational Events

  1. 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)
    Image
    Graph of the Motzkin polynomial, which is nonnegative but not a sum of squares.

    The study of nonnegative polynomials and sums of squares is a classical area of real algebraic geometry dating back to Hilbert’s 17th problem. It also has rich connections to real analysis via duality and moment problems. In the last 15 years, sums of squares relaxations have found a wide array of applications from very applied areas (e.g., robotics, computer vision, and machine learning) to theoretical applications (e.g., extremal combinatorics, theoretical computer science). Also, an intimate connection between sums of squares and classical algebraic geometry has been found. Work in this area requires a blend of ideas and techniques from algebraic geometry, convex geometry and representation theory. After an introduction to nonnegative polynomials, sums of squares and semidefinite optimization, we will focus on the following three topics:

    • Sums of squares on real varieties (sets defined by real polynomial equations) and connections with classical algebraic geometry.
    • Sums of squares method for proving graph density inequalities in extremal combinatorics. Here addition and multiplication take place in the gluing algebra of partially labelled graphs.
    • Sums of squares relaxations for convex hulls of real varieties and theta-bodies with applications in optimization.

    The summer school will give a self-contained introduction aimed at beginning graduate students, and introduce participants to the latest developments. In addition to attending the lectures, students will meet in intensive problem and discussion sessions that will explore and extend the topics developed in the lectures.

    Updated on Apr 07, 2022 02:41 PM PDT
  2. Summer Graduate School Tropical Geometry

    Organizers: Renzo Cavalieri (Colorado State University), Hannah Markwig (Eberhard-Karls-Universität Tübingen), Dhruv Ranganathan (University of Cambridge)
    Image
    A tropical stable map and the corresponding floor diagram

    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:

    1. Enumeration of tropical curves/ by Hannah Markwig
    2. Curve counting in tropical and algebraic geometry by Renzo Cavalieri
    3. Logarithmic geometry and stable map/s by Dhruv Ranganathan

    Updated on Aug 12, 2022 03:03 PM PDT
  3. Summer Graduate School Mathematics of Machine Learning (INdAM and Courant Institute)

    Organizers: Sebastien Bubeck (Microsoft Research)
    Image
    Popular visualization of the MNIST dataset

    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
  4. 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)
    Image

    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:

    1. 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.
    2. 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, simple-to-state 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 well-suited to rapidly put students in a position to approach related research questions.

    Updated on Aug 12, 2022 11:34 AM PDT
  5. Summer Graduate School MSRI-NCTS 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)
    Image
    Fluid-flow stream function color-coded by vorticity in 3D flat torus calculated by K. Nakai (The University of Tokyo)

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

    Updated on Aug 12, 2022 11:40 AM PDT
  6. 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 K-12 Teacher Leadership Program and the Workshop for Equity in Mathematics Education. PCMI includes numerous cross-program activities to help members from all these groups interact with one another.

    Updated on Feb 02, 2022 03:52 PM PST
  7. Summer Graduate School Metric Geometry and Geometric Analysis (Oxford, United Kingdom)

    Organizers: LEAD Cornelia Drutu (University of Oxford), Panos Papazoglou (University of Oxford)
    Cornelia picture 2
    Several geometric ideas in the context of a surface: hyperbolic metric, CAT(0) inequality, Gromov hyperbolicity/coarse median geometry, nonpositively-curved square tiling, Besikovitch inequality. (Picture by M. Hagen and A. Sisto.)

    The purpose of the summer school is to introduce graduate students to key mainstream directions in the recent development of geometry, which sprang from Riemannian Geometry in an attempt to use its methods in various contexts of non-smooth geometry. This concerns recent developments in metric generalizations of the theory of nonpositively curved spaces and discretizations of methods in geometry, geometric measure theory and global analysis. The metric geometry perspective gave rise to new results and problems in Riemannian Geometry as well.

    All these themes are intertwined and have developed either together or greatly influencing one another. The summer school will introduce some of the latest developments and the remaining open problems in these very modern areas, and will emphasize their synergy.

     

    Updated on Feb 14, 2022 12:29 PM PST
  8. 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)
    Image
    Image by Prof. Robert Lipshitz

    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 low-dimensional and symplectic topology. The two crowning achievements of these techniques so far are Manolescu's use of his Pin(2)-equivariant Seiberg--Witten Floer homotopy type to resolve the Triangulation Conjecture and Abouzaid-Blumberg's use of Floer homotopy theory and Morava K-theory 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
  9. Summer Graduate School Random Graphs

    Organizers: Louigi Addario-Berry (McGill University), Remco van der Hofstad (Technische Universiteit Eindhoven)
    2020 sgs random graphs proposal hofsatd.2018.12
    by DeDelphin Sénizergues

    The topic of random graphs is at the forefront of applied probability, and it is one of the central topics in multidisciplinary science where mathematical ideas are used to model and understand the real world. At the same time, random graphs pose challenging mathematical problems that have attracted the attention from probabilists and combinatorialists since the 1960, with the pioneering work of Erdös and Rényi. Around the turn of the millennium, very large data sets started to become available, and several applied disciplines started to realize that many real-world networks, even though they are from various different origins, share many fascinating features. In particular, many of such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scalefree, in the sense that there are enormous differences in the number of connections that their elements make. In particular, such networks are quite different from the classical random graph models, such as proposed by Erdös and Rényi.

    Updated on Jul 14, 2022 09:37 AM PDT
  10. 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)
    Image
    Algebraic Theory Of Differential And Difference Equations, Model Theory And Their Applications

    The purpose of the summer school will be to introduce graduate students to effective methods in algebraic theories of differential and difference equations with emphasis on their model-theoretic foundations and to demonstrate recent applications of these techniques to studying dynamic models arising in sciences. While these topics comprise a coherent and rich subject, they appear in graduate coursework in at best a piecemeal way, and then only as components of classes for other aims. With this Summer Graduate School, students will learn both the theoretical basis of differential and difference algebra and how to use these methods to solve practical problems. Beyond the lectures, the graduate students will meet daily in problem sessions and will participate in one-on-one mentoring sessions with the lecturers and organizers.

    Updated on Jul 22, 2022 09:57 AM PDT
  11. 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
  12. Summer Graduate School Geometric Flows (Crete, Greece)

    Organizers: Nicholas Alikakos (National and Kapodistrian University of Athens (University of Athens)), Panagiota Daskalopoulos (Columbia University)
    Image
    photo courtesy of Panagiota Daskalopoulos

    [The image on this vase from Minoan Crete, dated on 1500-2000 BC, resembles an ancient solution to the Curve shortening flow - one of the most basic geometric flows. The vase is at Heraklion Archaeological Museum]

    This summer graduate school is a collaboration between MSRI and the FORTH-IACM Institute in Crete. The purpose of the school is to introduce graduate students to some of the most important geometric evolution equations. 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 non-linear extrinsic flows such as the Gauss curvature flow. The lectures will also include geometric applications such as isoperimetric inequalities, topological applications such as the Poincaré onjecture, as well as recent important developments related to the study of singularities and ancient solutions.

    Updated on Jun 23, 2022 12:36 PM PDT
  13. MSRI-UP MSRI-UP 2022: Algebraic Methods in Mathematical Biology

    Organizers: LEAD Federico Ardila (San Francisco State University), Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI - Mathematical Sciences Research Institute), Rebecca Garcia (Sam Houston State University), Candice Price (Smith College), Anne Shiu (Texas A & M University; Texas A&M University)

    The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

    In 2022, MSRI-UP 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 May 31, 2022 02:30 PM PDT
  14. Summer Graduate School Integral Equations and Applications

    Organizers: Fioralba Cakoni (Rutgers University), Dorina Mitrea (Baylor University), Irina Mitrea (Temple University), Shari Moskow (Drexel University)
    Image
    L 2 Spectra of K for apertures π 15 , · · · 14π 15 , π

    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:

    1. introduce graduate students to the systematic study of integral equations;
    2. present some of the latest theoretical advancements in the field and open problems; and
    3. involve participants in a hands-on 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
  15. Workshop May 12, a Celebration for Women in Mathematics, year 2022

    Organizers: Ini Adinya (University of Ibadan), Maria-Grazia ASCENZI (University of California Los Angeles), Hajer Bahouri (Laboratoire Jacques-Louis Lions; Centre National de la Recherche Scientifique (CNRS)), Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), Lenore Blum (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 Fadipe-Joseph (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), Kuei-Nuan Lin (Pennsylvania State University), Liangbing Luo (University of Connecticut), LEAD Ornella Mattei (San Francisco State University), Betul Orcan-Ekmekci (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 in-person 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
  16. 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 K-12 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 K-12. 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
  17. Workshop Blackwell Tapia Conference 2021

    Organizers: David Banks (Duke University), Hélène Barcelo (MSRI - Mathematical Sciences Research Institute), 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 Blackwell-Tapia Conference (rescheduled from Fall 2020), will be held simultaneously at four locations nationwide.  The conference will celebrate the 2020 Blackwell-Tapia 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 Jersey

    Updated on Nov 08, 2021 10:30 AM PST
  18. Summer Graduate School Foundations and Frontiers of Probabilistic Proofs (Virtual School)

    Organizers: Alessandro Chiesa (University of California, Berkeley), Tom Gur (University of Warwick)
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    Several executions of a 3-dimensional sumcheck protocol with a random order of directions (thanks to Dev Ojha for creating the diagram)

    Proofs are at the foundations of mathematics. Viewed through the lens of theoretical computer science, verifying the correctness of a mathematical proof is a fundamental computational task. Indeed, the P versus NP problem, which deals precisely with the complexity of proof verification, is one of the most important open problems in all of mathematics.

    The complexity-theoretic study of proof verification has led to exciting reenvisionings of mathematical proofs. For example, probabilistically checkable proofs (PCPs) admit local-to-global structure that allows verifying a proof by reading only a minuscule portion of it. As another example, interactive proofs allow for verification via a conversation between a prover and a verifier, instead of the traditional static sequence of logical statements. The study of such proof systems has drawn upon deep mathematical tools to derive numerous applications to the theory of computation and beyond.

    In recent years, such probabilistic proofs received much attention due to a new motivation, delegation of computation, which is the emphasis of this summer school. This paradigm admits ultra-fast protocols that allow one party to check the correctness of the computation performed by another, untrusted, party. These protocols have even been realized within recently-deployed technology, for example, as part of cryptographic constructions known as succinct non-interactive arguments of knowledge (SNARKs).

    This summer school will provide an introduction to the field of probabilistic proofs and the beautiful mathematics behind it, as well as prepare students for conducting cutting-edge research in this area.

    Updated on Aug 11, 2021 12:27 PM PDT
  19. 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)
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    a random quasiconformal map obtained from Beltrami equation by randomly assigning the values of +-1/2 for the Beltrami coefficient on small squares subdividing the unit square

    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 semester-long 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
  20. 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)
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    Image by Nick Schmitt

    Figure 1. A rotationally symmetric solution to the self-duality equations on an open and dense subset of the torus. Singularities appear where the surface intersects the ideal boundary at infinity of the hyperbolic 3-space 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 low-dimensional 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 low-dimensional topology. By the end of the two-week program, the students will understand the relevant analytic and geometric aspects of several partial differential equations of current interest (including the Yang-Mills ASD equations, the Seiberg-Witten 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
  21. Summer Graduate School Mathematics of Big Data: Sketching and (Multi-) Linear Algebra (Virtual School)

    Organizers: LEAD Kenneth Clarkson (IBM Research Division), Lior Horesh (IBM Thomas J. Watson Research Center), Misha Kilmer (Tufts University), Tamara Kolda (Sandia National Laboratories; MathSci.ai), Shashanka Ubaru (IBM Thomas J. Watson Research Center)
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    This summer school will introduce graduate students to sketching-based approaches to computational linear and multi-linear 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 Mar 15, 2021 03:16 PM PDT
  22. MSRI-UP MSRI-UP 2021: Parking Functions: Choose your own adventure

    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 (University of Wisconsin-Milwaukee), Candice Price (Smith College)

    The MSRI-UP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.

    In 2021, MSRI-UP will focus on Parking Functions: Choose your own adventure. The research program will be led by Dr. Pamela E. Harris, Associate Professor of Mathematics at Williams College.

    Updated on Feb 05, 2021 01:42 PM PST
  23. Workshop [Online] Workshop on Mathematics and Racial Justice

    Organizers: Caleb Ashley (Boston College), Ron Buckmire (Occidental College), Duane Cooper (Morehouse College), Monica Jackson (American University), LEAD Omayra Ortega (Sonoma State University), LEAD Robin Wilson (California State Polytechnic University, Pomona)
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    The overarching goal of the Workshop on Mathematics and Racial Justice is to explore the role that mathematics plays in today’s movement for racial justice. For the purposes of this workshop, racial justice is the result of intentional, active and sustained anti-racist practices that identify and dismantle racist structures and policies that operate to oppress, disenfranchise, harm, and devalue Black people. This workshop will bring together mathematicians, statisticians, computer scientists, and STEM educators as well as members of the general public interested in using the tools of these disciplines to critically examine and eradicate racial disparities in society. Researchers with expertise or interest in problems at the intersection of mathematics, statistics and racial justice are encouraged to participate. This workshop will take place over two weeks and will include sessions on Bias in Algorithms and Technology; Fair Division, Allocation, and Representation; Public Health Disparities; and Racial Inequities in Mathematics Education.

    Updated on Jun 19, 2022 10:49 AM PDT
  24. Summer Graduate School Sparsity of Algebraic Points (Virtual School)

    Organizers: Philipp Habegger (University of Basel), LEAD Hector Pasten (Pontificia Universidad Católica de Chile)
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    The Corvaja-Zannier proof of Siegel's theorem using subspaces. Illustrated by Sofía Pastén Vásquez.

    The theory of Diophantine equations is understood today as the study of algebraic points in algebraic varieties, and it is often the case that algebraic points of arithmetic relevance are expected to be sparse.

    This summer school will introduce the participants to two of the main techniques in the subject: (i) the filtration method to prove algebraic degeneracy of integral points by means of the subspace theorem, leading to special cases of conjectures by Bombieri, Lang, and Vojta, and (ii) unlikely intersections through o-minimality and bi-algebraic geometry, leading to results in the context of the Manin-Mumford conjecture, the André-Oort conjecture, and generalizations. This SGS should provide an entry point to a very active research area in modern number theory.

    Updated on Mar 05, 2021 11:34 AM PST
  25. Summer Graduate School 2021 CRM-PIMS Summer School in Probability (Virtual School)

    Organizers: LEAD Louigi Addario-Berry (McGill University), Omer Angel (University of British Columbia), Alexander Fribergh (University of Montreal), Mathav Murugan (University of British Columbia), Edwin Perkins (University of British Columbia)
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    The Sherrington-Kirkpatrick model, aka the randomly-weighted complete graph. Edge weights are indicated using grayscale. Six distinguished vertices have been randomly chosen; edges between those vertices are shaded black to form a "hidden signal".

    The courses in this summer school focus on mathematical models of group dynamics, how to describe their dynamics and their scaling limits, and the connection to discrete and continuous optimization problems.

    The phrase "group dynamics" is used loosely here -- it may refer to species migration, the spread of a virus, or the propagation of electrons through an inhomogeneous medium, to name a few examples. Very commonly, such systems can be described via stochastic processes which approximately behave like the solution of an appropriate partial differential equation in the large-population limit.

    Updated on Aug 09, 2021 02:04 PM PDT
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