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  1. Program Mathematics and Computer Science of Market and Mechanism Design

    Organizers: Martin Bichler (TU München), Péter Biró (KRTK, Eotvos Lorand Research Network), Michal Feldman (Tel-Aviv University), Nicole Immorlica (Microsoft Research), LEAD Scott Kominers (Harvard Business School), Shengwu Li (Harvard University), Paul Milgrom (Stanford University), Alvin Roth (Stanford University), Eva Tardos (Cornell University)
    Gt mechanism design

    In recent years, economists and computer scientists have collaborated with mathematicians, operations research experts, and practitioners to improve the design and operations of real-world marketplaces. Such work relies on robust feedback between theory and practice, inspiring new mathematics closely linked – and directly applicable – to market and mechanism design questions. This cross-disciplinary program seeks to expand the domains in which existing market design solutions can be applied; address foundational questions regarding our ways of developing and evaluating mechanisms; and build useful analytic frameworks for applying theory to practical marketplace design.

    Updated on Oct 18, 2023 09:04 AM PDT
  2. Program Algorithms, Fairness, and Equity

    Organizers: Vincent Conitzer (Carnegie Mellon University), Moon Duchin (Tufts University), Bettina Klaus (University of Lausanne), Jonathan Mattingly (Duke University), LEAD Wesley Pegden (Carnegie Mellon University)
    Image
    <p>A graphical representation of a Markov Chain fairness analysis of a political districting in North Carolina from Chin, Herschlag, Mattingly</p>

    This program aims to bring together researchers working at the interface of fairness and computation. This interface has been the site of intensive research effort in mechanism design, in research on partitioning problems related to political districting problems, and in research on ways to address issues of fairness and equity in the context of machine learning algorithms.

    These areas each approach the relationship between mathematics and fairness from a distinct perspective. In mechanism design, algorithms are a tool to achieve outcomes with mathematical guarantees of various notions of fairness. In machine learning, we perceive failures of fairness as an undesirable side effect of learning approaches, and seek mathematical approaches to understand and mitigate these failures. And in partitioning problems like political districting, we often seek mathematical tools to evaluate the fairness of human decisions.

    This program will explore progress in these areas while also providing a venue for overlapping perspectives. The topics workshop “Randomization, neutrality, and fairness” will explore the common role randomness and probability has played in these lines of work.

    Updated on Aug 24, 2023 07:26 AM PDT
  3. Program Complementary Program 2023-24

    The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program. 

    Updated on Sep 26, 2023 11:36 AM PDT
  4. Workshop Hot Topics: Recent Progress in Deterministic and Stochastic Fluid-Structure Interaction

    Organizers: Martina Bukac (University of Notre Dame), Suncica Canic (University of California, Berkeley), LEAD Jeffrey Kuan (University of Maryland), Justin Webster (University of Maryland, Baltimore County)
    Aaadisplacement
    Blood flow and structure displacement in an Aortic Abdominal Aneurysm

    This workshop will focus on the coupled dynamical interaction between fluids and elastic/poroelastic structures, with an emphasis on the most recent and cutting-edge mathematical advances in deterministic and stochastic fluid-structure interaction. The goal of this workshop is to bring together a diverse group of mathematicians in the fields of analysis, modeling, numerics, stochastics, and real-world applications in order to showcase an interdisciplinary approach to the study of coupled fluid-structure systems. A major component of this workshop will be to encourage active participation of early career researchers, such as graduate students and postdocs, and foster synergistic collaboration with established leaders in the field.

    Updated on Dec 06, 2023 01:25 PM PST
  1. Seminar Social Choice Seminar

    Created on Sep 12, 2023 08:09 AM PDT
  2. Seminar Network Science Lunch

    Created on Nov 15, 2023 09:23 AM PST
  3. Seminar Social Choice Seminar

    Created on Sep 12, 2023 08:09 AM PDT
  4. Seminar Network Science Lunch

    Created on Nov 15, 2023 09:23 AM PST
  5. Program Commutative Algebra

    Organizers: Aldo Conca (Università di Genova), 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), Claire Voisin (Collège de France; Institut de Mathématiques de Jussieu)
    9 points theorem
    Image for theorem about 9 point on cubic curve, the special case of Cayley–Bacharach theorem.

    Commutative algebra is, in its essence, the study of algebraic objects, such as rings and modules over them, arising from polynomials and integral numbers.     It has numerous connections to other fields of mathematics including algebraic geometry, algebraic number theory, algebraic topology and algebraic combinatorics. Commutative Algebra has witnessed a number of spectacular developments in recent years, including the resolution of long-standing problems, with new techniques and perspectives leading to an extraordinary transformation in the field. The main focus of the program will be on these developments. These include the recent solution of Hochster's direct summand conjecture in mixed characteristic that employs the theory of perfectoid spaces, a new approach to the Buchsbaum--Eisenbud--Horrocks conjecture on the Betti numbers of modules of finite length, recent progress on the study of Castelnuovo--Mumford regularity, the proof of Stillman's conjecture and ongoing work on its effectiveness, a novel strategy to Green's conjecture on the syzygies of canonical curves based on the study of Koszul modules and their generalizations, new developments in the study of various types of multiplicities, theoretical and computational aspects of Gröbner bases, and the implicitization problem for Rees algebras and its applications.

    Updated on May 24, 2022 10:29 AM PDT
  6. Program Noncommutative Algebraic Geometry

    Organizers: Wendy Lowen (Universiteit Antwerpen), Alex Perry (University of Michigan), LEAD Alexander Polishchuk (University of Oregon), Susan Sierra (University of Edinburgh), Michel Van den Bergh (Hasselt University), Špela Špenko (Université Libre de Bruxelles)
    Image
    Optical illusion staircase

    Derived categories of coherent sheaves on algebraic varieties were originally conceived as technical tools for studying cohomology, but have since become central objects in fields ranging from algebraic geometry to mathematical physics, symplectic geometry, and representation theory. Noncommutative algebraic geometry is based on the idea that any category sufficiently similar to the derived category of a variety should be regarded as (the derived category of) a “noncommutative algebraic variety”; examples include semiorthogonal components of derived categories, categories of matrix factorizations, and derived categories of noncommutative dg-algebras. This perspective has led to progress on old problems, as well as surprising connections between seemingly unrelated areas. In recent years there have been great advances in this domain, including new tools for constructing semiorthogonal decompositions and derived equivalences, progress on conjectures relating birational geometry and singularities to derived categories, constructions of moduli spaces from noncommutative varieties, and instances of homological mirror symmetry for noncommutative varieties. The goal of this program is to explore and expand upon these developments. 

    Updated on May 19, 2022 01:51 PM PDT
  7. Workshop Connections Workshop: Commutative Algebra

    Organizers: Christine Berkesch (University of Minnesota), Louiza Fouli (New Mexico State University), Maria Evelina Rossi (Università di Genova), LEAD Alexandra Seceleanu (University of Nebraska)

    This two-day workshop will feature the work of mathematicians in commutative algebra who identify as women or another marginalized gender. The talks will be appropriate for graduate students, post-docs, and researchers in areas related to the program. This meeting aims to support young researchers. The format will include plenary talks, poster sessions, panel discussions, as well as the opportunity for informal discussions and connections.  The workshop is open to all mathematicians, and members of historically excluded groups and identities are especially encouraged to attend.

    Updated on Nov 04, 2022 04:05 PM PDT
  8. Workshop Introductory Workshop: Commutative Algebra

    Organizers: Srikanth Iyengar (University of Utah), Claudia Miller (Syracuse University), Claudia Polini (University of Notre Dame), LEAD Anurag Singh (University of Utah)
    Msri 1053 image
    Fractal behavior of local cohomology. For details, see arXiv:2210.03656 by Gao and Raicu

    The Introductory Workshop will feature lecture series devoted to some recent breakthrough results in commutative algebra, and to new developments in core areas of the field.  It will also highlight links to other areas such as arithmetic geometry, representation theory, noncommutative geometry, and singularity theory.

    Updated on Oct 31, 2022 04:02 PM PDT
  9. Workshop Connections Workshop: Noncommutative Algebraic Geometry

    Organizers: Rina Anno (Kansas State University), Elizabeth Gasparim (Universidad Católica del Norte), LEAD Alice Rizzardo (University of Liverpool)
    Connections1

    This two-day workshop will feature the work of mathematicians in noncommutative geometry who identify as women or another marginalized gender. The talks will be appropriate for graduate students, post-docs, and researchers in areas related to the program. This meeting aims to support young researchers.

    The workshop will focus on recent developments in noncommutative algebraic geometry including Derived Algebraic Geometry, Categorical and Noncommutative Resolutions, Deformation Theory, and Enumerative Geometry.

    The format will include plenary talks, a poster session, panel discussions, as well as the opportunity for informal discussions and connections in noncommutative geometry. The workshop is open to all mathematicians, and members of historically excluded groups and identities are especially encouraged to attend.

    Updated on Feb 06, 2023 11:36 AM PST
  10. Workshop Introductory Workshop: Noncommutative Algebraic Geometry

    Organizers: Nicolas Addington (University of Oregon), LEAD David Favero (University of Minnesota), Wendy Lowen (Universiteit Antwerpen), Alice Rizzardo (University of Liverpool)
    Image0
    A paper fortune teller illustrating the Atiyah flop.

    This introductory workshop will consist of a combination of minicourses addressing core topics in noncommutative algebraic geometry and research lectures describing recent developments in the field.  The workshop will focus on subjects connected to algebraic geometry, category theory, and mirror symmetry such as categorical and noncommutative resolutions, deformation theory, derived categories in algebraic geometry, derived algebraic geometry, infinity categories, and enumerative geometry.

    Updated on Feb 22, 2023 03:13 PM PST
  11. Workshop Hot Topics: Artin Groups and Arrangements - Topology, Geometry, and Combinatorics

    Organizers: Christin Bibby (Louisiana State University), Ruth Charney (Brandeis University), Giovanni Paolini (California Institute of Technology), Mario Salvetti (Università di Pisa)
    Affine arrangement
    The affine line arrangement of type C with different lattices and toric arrangements arising from it.

    This workshop brings together experts from different areas to discuss and foster collaboration on several topics of current interest related to Artin groups such as the K(π, 1) conjecture, hyperplane arrangements and abelian arrangements, combinatorial structures associated with dual Coxeter systems, and complexes of nonpositive curvature.

    Updated on Sep 21, 2023 03:05 PM PDT
  12. Workshop Critical Issues in Mathematics Education 2024: Bringing Innovation to Scale: Teaching-Focused Faculty as Change Agents

    Organizers: Debra Carney (Colorado School of Mines), David Kung (University of Texas, Austin), Gavin LaRose (University of Michigan), Mary Pilgrim (San Diego State University), Chris Rasmussen (San Diego State University), Natasha Speer (University of Maine), Cristina Villalobos (University of Texas Rio Grande Valley)
    Image

    The undergraduate mathematics education system remains a huge barrier to college completion and to equity in higher education. The problem in entry level mathematics courses is not a lack of innovation. Numerous projects and institutions have created, piloted, and occasionally replicated effective reform efforts that overcame particular challenges, like the need to improve pedagogical practices or attend to gender equity. The biggest barrier to systemic reform – implementing many of these research-backed innovations at scale – is a structural one, particularly at large research-focused institutions. This workshop will bring together a group of stakeholders to explore a new avenue for change, the rise of teaching-focused faculty at research-intensive institutions who increasingly influence introductory coursework. By creating a network that connects these faculty across institutions, change at scale across 50, 100, or even more institutions becomes possible – on issues ranging from pedagogy to equity to curricular innovation. Creating such structures would also allow for bringing future innovations to scale much more quickly than is currently possible.

    Updated on Nov 22, 2023 01:07 PM PST
  13. Workshop Recent Developments in Noncommutative Algebraic Geometry

    Organizers: Arend Bayer (University of Edinburgh), Graham Leuschke (Syracuse University), Alexander Polishchuk (University of Oregon), Susan Sierra (University of Edinburgh), Gregory Stevenson (Aarhus University), Špela Špenko (Université Libre de Bruxelles)
    Image
    Optical illusion staircase

    This workshop will give an overview of recent developments in non-commutative algebraic geometry, including NC projective AG, NC resolutions, semiorthogonal decompositions, enhancements of derived categories, and connections to homological mirror symmetry, to enumerative AG, to moduli spaces and to birational geometry. It will in particular focus on speakers who have built new bridges between these topics.

    Updated on Nov 30, 2022 09:03 AM PST
  14. Workshop Recent Developments in Commutative Algebra

    Organizers: Daniel Erman (University of Hawaii at Manoa), Linquan Ma (Purdue University), LEAD Karl Schwede (University of Utah), Karen Smith (University of Michigan), Andrew Snowden (University of Michigan), Irena Swanson (Purdue University)

    Many long-standing conjectures in commutative algebra have been solved in recent years, often through the introduction of new methods that are quickly becoming central to the field.  This workshop will bring together a wide array of researchers in commutative algebra and related fields, with the goal of forging new connections among topics, and with a particular emphasis on transformative new methods.

    Created on Jul 27, 2022 02:01 PM PDT
  15. Workshop Advances in Lie Theory, Representation Theory, and Combinatorics: Inspired by the work of Georgia M. Benkart

    Organizers: Hélène Barcelo (MSRI / Simons Laufer Mathematical Sciences Institute (SLMath)), Ellen Kirkman (Wake Forest University), Gail Letzter (Retired ), Daniel Nakano (University of Georgia), Arun Ram (University of Melbourne)
    Image

    This workshop will have a view to the future of a broad spectrum of topics including

    • structure and classification of finite dimensional Lie algebras and superalgebras in characteristic p
    • structure of infinite dimensional Lie algebras and their representations
    • deformation theory of algebras, double constructions and elemental Lie algebras
    • diagram algebras and combinatorial representation theory
    • algebraic combinatorics of groups of Lie type:characters, Schur-Weyl duality, Bratteli diagrams, and McKay correspondences
    • quantum groups and crystal bases, particularly for superalgebras and affine algebras
    • examples of fusion categories arising from representations of Drinfeld doubles and other algebras
    • cohomology for finite tensor categories with applications to its underlying geometry

    This meeting will feature principal contributors in these areas in a celebration of the work of Georgia Benkart. With the same focus and tenacity that Georgia always had, we will strive to provide a conference full of beautiful mathematics, incredible inspiration, and the warmth of Georgia’s welcoming personality to our field and our community.

    Updated on Aug 24, 2023 09:01 AM PDT
  16. Summer Graduate School Séminaire de Mathématiques Supérieures 2024: Flows and Variational Methods in Riemannian and Complex Geometry: Classical and Modern Methods (Montréal, Canada)

    Organizers: Vestislav Apostolov (Université du Québec à Montréal), Eleonora Di Nezza (Institut de Mathématiques de Jussieu), Pengfei Guan (McGill University), Spiro Karigiannis (University of Waterloo), Julien Keller (Université du Québec à Montréal), Alina Stancu (Concordia University), Valentino Tosatti (New York University, Courant Institute)
    1061 image

    This school will present various developments in Riemannian and Kähler geometry around the notion of curvature seen as a tool to describe and understand the geometry of the objects. The school will give graduate students the opportunity to learn key ideas and techniques of the field, with an emphasis on solidifying foundations in view of potential future research. The first week will be centered around the question of the existence of Kähler metrics with special curvature properties and the famous Yau-Tian-Donaldson conjecture. The second week will focus on geometric flows in Riemannian and complex geometry. 

    Updated on Oct 02, 2023 06:32 AM PDT
  17. Summer Research in Mathematics 2024 Summer Research in Mathematics

    MSRI/SLMath's Summer Research in Mathematics program provides space, funding, and the opportunity for in-person collaboration to small groups of mathematicians, especially women and gender-expansive individuals, whose ongoing research may have been disproportionately affected by various obstacles including family obligations, professional isolation, or access to funding. Through this effort, MSRI/SLMath aims to mitigate the obstacles faced by these groups, improve the odds of research project completion, and deepen their research experience. The ultimate goal of this program is to enhance the mathematical sciences as a whole by positively affecting the research and careers of all of its participants and assisting their efforts to maintain involvement in the research community.

    The ultimate goal of this program is to enhance the mathematical sciences as a whole by positively affecting the research and careers of all of its participants and assisting their efforts to maintain involvement in the research community.

    Updated on Sep 14, 2023 09:46 AM PDT
  18. MSRI-UP MSRI-UP 2024: Mathematical Endocrinology

    Organizers: Federico Ardila (San Francisco State University), Alexander Diaz-Lopez (Villanova University), Maria Mercedes Franco (Queensborough Community College (CUNY)), Rebecca Garcia (Colorado College), LEAD Candice Price (Smith College), Robin Wilson (Loyola Marymount 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 2024, MSRI-UP will focus on Mathematical Endocrinology. The research program will be led by Dr. Erica J. Graham, Associate Professor in the Department of Mathematics at Bryn Mawr College.

    Updated on Dec 05, 2023 09:38 AM PST
  19. Summer Graduate School Particle interactive systems: Analysis and computational methods (SLMath)

    Organizers: LEAD Irene M. Gamba (University of Texas, Austin), Francois Golse (École Polytechnique), LEAD Qin Li (University of Wisconsin-Madison), Chiara Saffirio (Universität Basel)
    Particle interactions

    This summer school will focus on the introductory notions related to the passage of Newtonian and quantum many-body dynamics to kinetic collisional models of Boltzmann flow models arising in statistical sciences in connection to model reductions when continuum macro dynamics arises; and their numerical schemes associated to transport of kinetic processes in classical and data driven mean field dynamics incorporating recent tools from computational kinetics and data science tools. There will be two sets of lectures: “From Newton to Boltzmann to Fluid dynamics”, and “Kinetic collisional theory in mean field regimes: analysis, discrete approximations, and applications”. Each lecture series will be accompanied by a collaboration session, led by the lecturer and teaching assistants. The purpose of the collaboration sessions is to encourage and strengthen higher-level thinking of the materials taught in the lectures and to direct further reading for interested students. Interactive learning activities will be conducted. For example, students will be given problem sets associated with the lectures and will work in small groups to discuss concepts and/or find solutions to assigned problems. The students will also be encouraged to give oral or poster presentations on their solutions or other materials relevant to the course.

    Updated on Oct 02, 2023 06:33 AM PDT
  20. Summer Graduate School Special Geometric Structures and Analysis (St. Mary's College)

    Organizers: Costante Bellettini (University College London), LEAD Eleonora Di Nezza (Institut de Mathématiques de Jussieu), Song Sun (University of California, Berkeley)
    1066 image
    a Calabi-Yau manifold

    This summer school will serve as an introduction to the SLMath program "Special geometric structures and analysis". There will be two mini-courses: one in Geometric Measure theory and the other in Microlocal Analysis. The aim is to give the basic notions of two subjects also treated during the program.

    Updated on Oct 02, 2023 06:33 AM PDT
  21. African Diaspora Joint Mathematics ADJOINT 2024

    ADJOINT is a yearlong program that provides opportunities for U.S. mathematicians – especially those from the African Diaspora – to conduct collaborative research on topics at the forefront of mathematical and statistical research. Participants will spend two weeks taking part in an intensive collaborative summer session at SLMath (formerly MSRI). The two-week summer session for ADJOINT 2024 will take place June 24 to July 5, 2024 in Berkeley, California. Researchers can participate in either of the following ways: (1) joining ADJOINT small groups under the guidance of some of the nation's foremost mathematicians and statisticians to expand their research portfolio into new areas, or (2) applying to Self-ADJOINT as part of an existing or newly-formed independent research group to work on a new or established research project. Throughout the following academic year, the program provides conference and travel support to increase opportunities for collaboration, maximize researcher visibility, and engender a sense of community among participants. 

    Updated on Oct 02, 2023 11:15 AM PDT
  22. Summer Graduate School Introduction to Quantum-Safe Cryptography (IBM Zurich)

    Organizers: Jonathan Bootle (IBM Zürich Research Laboratory), Luca De Feo (IBM Zürich Research Laboratory)
    1068 image2

    This two week summer school, jointly organized by SLMath with IBM Zurich, will introduce students to the mathematics and algorithms used in the design and analysis of quantum-safe cryptosystems. Each week will be dedicated to two of the four families of quantum-safe schemes.

    Updated on Oct 19, 2023 01:07 PM PDT
  23. Summer Graduate School Stochastic Quantization (SLMath)

    Organizers: Massimiliano Gubinelli (University of Oxford), Martina Hofmanova (Universität Bielefeld), LEAD Hao Shen (University of Wisconsin-Madison), Lorenzo Zambotti (Sorbonne Université)
    Wordcloud

    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 who are perhaps familiar with some but not all of these subjects and teach them how to integrate these different tools to solve cutting-edge problems of Euclidean quantum field theory.

    Updated on Oct 02, 2023 06:31 AM PDT
  24. Summer Graduate School Koszul Duality in the Local Langlands Program (St. Mary's College)

    Organizers: Clifton Cunningham (University of Calgary), LEAD Sarah Dijols (University of Calgary)
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    This summer school provides the mathematical background to recognize Koszul duality in representation theory. The school is especially oriented toward applications in the local Langlands program, with an emphasis on real groups. As Koszul duality patterns have been initially observed in the context of Hecke algebras, our school will also introduce the students to Hecke algebras and their categorifications.

    Updated on Oct 02, 2023 06:34 AM PDT
  25. Summer Graduate School H-principle (Sendai, Japan)

    Organizers: Emmy Murphy (Princeton University), Takashi Tsuboi (RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program)
    1074 image
    The image of a large sphere isometrically embedded into a small space through a C^1 embedding. (Attributions: E. Bartzos, V. Borrelli, R. Denis, F. Lazarus, D. Rohmer, B. Thibert)

    This two week summer school, jointly organized by SLMath with RIKEN, will introduce graduate students to the theory of h-principles.  After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, fluid dynamics, and foliation theory.

    h-principles in smooth topology (Emmy Murphy)
    Riemannian geometry and applications to fluid dynamics (Dominik Inauen)
    Contact and symplectic flexibility (Emmy Murphy)
    Foliation theory and diffeomorphism groups (Takashi Tsuboi)

    Updated on Oct 02, 2023 06:34 AM PDT
  26. Summer Graduate School Introduction to the Theory of Algebraic Curves (UC Berkeley)

    Organizers: Izzet Coskun (University of Illinois, Chicago), Eric Larson (Brown University), LEAD Hannah Larson (University of California, Berkeley), Isabel Vogt (Brown University)
    1067 image

    In the last few years, there have been extraordinary developments in many aspects of curve theory. Beginning with many examples in low genus, this summer school will introduce the participants to the background behind these developments in the following areas:

    1. moduli spaces of stable curves
    2. Brill–Noether theory
    3. the extrinsic geometry of the curves in projective space

    We will also include an introduction to some open problems at the forefront of these active areas.

    Updated on Oct 02, 2023 06:35 AM PDT
  27. Program Quantum Symmetries Reunion

    Program picture
    The study of tensor categories involves the interplay of representation theory, combinatorics, number theory, and low dimensional topology (from a string diagram calculation, describing the 3-dimensional bordism 2-category [arXiv:1411.0945]).

    Symmetry, as formalized by group theory, is ubiquitous across mathematics and science. Classical examples include point groups in crystallography, Noether's theorem relating differentiable symmetries and conserved quantities, and the classification of fundamental particles according to irreducible representations of the Poincaré group and the internal symmetry groups of the standard model. However, in some quantum settings, the notion of a group is no longer enough to capture all symmetries. Important motivating examples include Galois-like symmetries of von Neumann algebras, anyonic particles in condensed matter physics, and deformations of universal enveloping algebras. The language of tensor categories provides a unified framework to discuss these notions of quantum symmetry.

    Updated on Sep 14, 2023 04:03 AM PDT
  28. Summer Graduate School Mathematics of General Relativity and Fluids (FORTH, Greece)

    Organizers: LEAD Mihalis Dafermos (Princeton University), Grigorios Fournodavlos (University of Crete), Juhi Jang (University of Southern California), Igor Rodnianski (Princeton University)
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    ALCF Visualization and Data Analytics Team; Adam Burrows and the Princeton Supernova Theory Group, Princeton University

    This summer school will give an accessible introduction to the mathematical study of general relativity, a field which in the past has had barriers to entry due to its interdisciplinary nature, and whose study has been concentrated at specific institutions, to a wider audience of students studying at institutions throughout the U.S., Europe and Greece. Another goal of the summer school will be to demonstrate the common underlying mathematical themes in many problems which traditionally have been studied by separate research communities.

    Updated on Oct 02, 2023 06:35 AM PDT
  29. Summer Graduate School Structure and representation theory of reductive p-adic groups (St. Mary's College)

    Organizers: LEAD Jessica Fintzen (Universität Bonn), LEAD Tasho Kaletha (University of Michigan)
    1034 image

    The summer school is an introduction to the representation theory and harmonic analysis of reductive p-adic groups and will feature several lecture series covering the structure of reductive p-adic groups, the classification of their representations, key results from harmonic analysis, an introduction to the local Langlands conjectures, as well as connections to automorphic forms, real reductive groups, and finite groups of Lie type. Active engagement of the student through problem and Q&A sessions will be an important component. The goal is to equip students with knowledge that would help them to perform research in this area or apply these tools in nearby areas.

    Updated on Oct 02, 2023 06:35 AM PDT
  30. Summer Graduate School Analysis of Partial Differential Equations (Okinawa Institute of Science and Technology)

    Organizers: Ugur Abdulla (Okinawa Institute of Science and Technology), Gui-Qiang Chen (University of Oxford)

    This two week summer school, jointly organized by SLMath with OIST, will offer the following two mini-courses:

    1. Measure-theoretical analysis, divergence-measure fields, and nonlinear PDEs of divergence form
      This course will present some recent developments in the theory of divergence-measure fields via measure-theoretic analysis and its applications to the analysis of nonlinear PDEs of conservative form – nonlinear conservation laws.
    2. Perron’s method and Wiener-type criteria in the potential theory of elliptic and parabolic PDEs
      This course will present some recent developments precisely characterizing the regularity of the point at ∞ for second order elliptic and parabolic PDEs and broadly extending the role of the Wiener test in classical analysis.

    Updated on Oct 24, 2023 03:34 PM PDT
  31. Summer Graduate School Mathematical Spin Glass Theory (Courant, NY)

    Organizers: Antonio Auffinger (Northwestern University), Wei-Kuo Chen (University of Minnesota), LEAD Eliran Subag (Weizmann Institute of Science)
    1063 image
    An ultrametric matrix with 4-step replica symmetry breaking

    While their original aim was to explain the strange behavior of certain magnetic alloys, the study of spin glass models has led to a far-reaching and beautiful physical theory whose techniques have been applied to a myriad of problems in theoretical computer science, statistics, optimization and biology. As many of the physical predictions can be formulated as purely mathematical questions, often extremely hard, about large random systems in high dimensions, in recent decades a new area of research has emerged in probability theory around these problems.

    Mathematically, a mean-field spin glass model is a Gaussian process (random function) on the discrete hypercube or the sphere in high dimensions. A fundamental challenge in their analysis is, roughly speaking, to understand the size and structure of their super-level sets as the dimension tends to infinity, which are often studied through smooth objects like the free energy and Gibbs measure whose origin is in statistical physics. The aim of the summer school is to introduce students to landmark results on the latter while emphasizing the techniques an ideas that were developed to obtain them, as well as exposing the students to some recent research topics.

    Updated on Oct 02, 2023 06:36 AM PDT
  32. Program New Frontiers in Curvature: Flows, General Relativity, Minimal Submanifolds, and Symmetry

    Organizers: LEAD Ailana Fraser (University of British Columbia), Lan-Hsuan Huang (University of Connecticut), Richard Schoen (University of California, Irvine), LEAD Catherine Searle (Wichita State University), Lu Wang (Yale University), Guofang Wei (University of California, Santa Barbara)
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    Soap bubble: equilibrium solution of the mean curvature flow and constant curvature surface.

    Geometry, PDE, and Relativity are subjects that have shown intriguing interactions in the past several decades, while simultaneously diverging, each with an ever growing number of branches. Recently, several major breakthroughs have been made in each of these fields using techniques and ideas from the others. 

    This program is aimed at connecting various branches of Geometry, PDE, and Relativity and at enhancing collaborations across these disciplines and will include four main topics: Geometric Flows, Geometric problems in Mathematical Relativity, Global Riemannian Geometry, and Minimal Submanifolds. Specifically the program focuses on a central goal, which is to advance our knowledge toward Riemannian (sub)manifolds under geometric conditions, such as curvature lower bounds, by developing techniques in, for example, geometric flows and minimal submanifolds and further fostering new connections.

    Updated on Nov 17, 2022 10:10 AM PST
  33. Program Special Geometric Structures and Analysis

    Organizers: Eleonora Di Nezza (Institut de Mathématiques de Jussieu), LEAD Mark Haskins (Duke University), Tristan Riviere (ETH Zurich), Song Sun (University of California, Berkeley), Xuwen Zhu (Northeastern University)
    Image
    “Plateau’s Memory ” (by A. van der Net): A soap film with singularities

    This program sits at the intersection between differential geometry and analysis but also connects to several other adjacent mathematical fields and to theoretical physics. Differential geometry aims to answer questions about very regular geometric objects (smooth Riemannian manifolds) using the tools of differential calculus. A fundamental object is the curvature tensor of a Riemannian metric: an algebraically complicated object that involves 2nd partial derivatives of the metric. Many questions in differential geometry can therefore be translated into questions about the existence or properties of the solutions of systems of (often) nonlinear partial differential equations (PDEs). The PDE systems that arise in geometry have historically stimulated the development of powerful new analytic methods. In most cases the nonlinearity of these systems makes ‘closed form’ expressions for a solution impossible: instead more abstract methods must be employed.

    Updated on Nov 10, 2022 04:20 PM PST
  34. Program Complementary Program 2024-25

    The Complementary Program has a limited number of memberships that are open to mathematicians whose interests are not closely related to the core programs; special consideration is given to mathematicians who are partners of an invited member of a core program. 

    Updated on Nov 03, 2023 03:25 PM PDT
  35. Workshop Connections Workshop: New Frontiers in Curvature & Special Geometric Structures and Analysis

    Organizers: Sun-Yung Chang (Princeton University), Lan-Hsuan Huang (University of Connecticut), Chikako Mese (Johns Hopkins University), Ilaria Mondello (Université Paris-Est Créteil Val-de-Marne), LEAD Guofang Wei (University of California, Santa Barbara), LEAD Xuwen Zhu (Northeastern University)
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    Geosurface

    This three-day workshop will consist of various talks given by prominent female mathematicians on topics of differential geometry and geometric analysis. These will be appropriate for graduate students, post-docs, and researchers in areas related to the two programs.  The workshop will also include activities to promote interaction and connection between participants. This workshop is open to all mathematicians.

    Updated on Sep 22, 2023 09:28 AM PDT
  36. Workshop Introductory Workshop: New Frontiers in Curvature

    Organizers: Ailana Fraser (University of British Columbia), Karsten Grove (University of Notre Dame), Richard Schoen (University of California, Irvine), Catherine Searle (Wichita State University), LEAD Lu Wang (Yale University)
    Starter project   2019 11 25 12.18.26
    The spatial Schwarzschild space with minimal surface boundary foliated by the inverse mean curvature flow

    This workshop will include introductory lectures on each of the four main topics of the program: geometric flows, geometric problems in mathematical relativity, global Riemannian geometry, and minimal submanifolds. The workshop will also have semi-expository lectures on recent advances and breakthroughs involving interactions between the four main topics. This will set the stage and provide important context for the semester-long program itself. 

    Updated on Aug 25, 2023 05:46 AM PDT
  37. Workshop Introductory Workshop: Special Geometric Structures and Analysis

    Organizers: Anda Degeratu (Universität Stuttgart), LEAD Eleonora Di Nezza (Institut de Mathématiques de Jussieu), Luca Spolaor (University of California, San Diego), Song Sun (University of California, Berkeley)
    Msri intro w  picture

    This workshop aims to prepare the participants for the main program: Special Geometric Structures and Analysis.
    There will be introductory lectures to recent results in geometry and analysis; more precisely in Kähler geometry, special holonomy, microlocal analysis and geometric measure theory

    Updated on Jun 12, 2023 09:49 AM PDT
  38. Workshop Recent progress on geometric analysis and Riemannian geometry

    Organizers: LEAD Lan-Hsuan Huang (University of Connecticut), Bruce Kleiner (New York University, Courant Institute), Andre Neves (University of Chicago), Richard Schoen (University of California, Irvine), LEAD Catherine Searle (Wichita State University), Guofang Wei (University of California, Santa Barbara)
    Hopf fibration
    <p>The Hopf fibration of <span class="math-tex">\(S^3 \space by \space S^1\)</span></p>

    This workshop will bring together researchers at the frontiers of geometric analysis and Riemannian geometry, with a focus on recent advances on geometric flows, geometric problems in mathematical relativity, global Riemannian geometry, and minimal submanifolds. These areas have shown highly intriguing interactions in recent years and we expect this workshop will provide a unique opportunity to facilitate these emerging links.

    Updated on Nov 07, 2023 01:00 PM PST
  39. Program Probability and Statistics of Discrete Structures

    Organizers: Louigi Addario-Berry (McGill University), Christina Goldschmidt (University of Oxford), Po-Ling Loh (University of Cambridge), Gabor Lugosi (ICREA), Dana Randall (Georgia Institute of Technology), LEAD Remco van der Hofstad (Technische Universiteit Eindhoven)
    Psds image small
    The minimum spanning tree of 100,000 uniformly random points. Colors encode graph distance from the root, which is red. Black points are those whose removal would disconnect at least 5% of the points from the rest.

    Random graphs and related random discrete structures lie at the forefront of applied probability and statistics, and are core topics across a wide range of scientific disciplines where mathematical ideas are used to model and understand real-world networks. At the same time, random graphs pose challenging mathematical and algorithmic problems that have attracted attention from probabilists and combinatorialists since at least 1960, following the pioneering work of Erdős and Renyi.

    Around the turn of the millennium, as very large data sets became available, several applied disciplines started to realize that many real-world networks, even though they are from various origins, share fascinating features. In particular, many such networks are small worlds, meaning that graph distances in them are typically quite small, and they are scale-free, in the sense that the number of connections made by their elements is extremely heterogeneous. This program is devoted to the study of the probabilistic and statistical properties of such networks. Central tools include graphon theory for dense graphs, local weak convergence for sparse graphs, and scaling limits for the critical behavior of graphs or stochastic processes on them. The program is aimed at pure and applied mathematicians interested in network problems.

    Updated on Sep 14, 2023 10:08 AM PDT
  40. Program Extremal Combinatorics

    Organizers: LEAD David Conlon (California Institute of Technology), LEAD Jacob Fox (Stanford University), Penny Haxell (University of Waterloo), Janos Pach (Alfréd Rényi Institute of Mathematics), Maya Stein (Universidad de Chile), Andrew Suk (University of California, San Diego)
    Logomsriextcomb

    Extremal combinatorics concerns itself with problems about how large or small a finite collection of objects can be while satisfying certain conditions. Questions of this type arise naturally across mathematics, so this area has close connections and interactions with a broad array of other fields, including number theory, group theory, model theory, probability, statistical physics, optimization, and theoretical computer science.

    The area has seen huge growth in the twenty-first century and, particularly in recent years, there has been a steady stream of solutions to important longstanding problems and many powerful new methods have been introduced. These advances include improvements in absorption techniques which have facilitated the proof of the existence of designs and related objects, the breakthrough on the sunflower conjecture whose further development eventually led to the proof of the Kahn–Kalai conjecture in discrete probability and the discovery of interactions between spectral graph theory and the study of equiangular lines in discrete geometry. These and other groundbreaking advances will be the central theme of the semester program on “Extremal Combinatorics” at SLMath.

    In this program, we will bring together experts as well as enthusiastic young researchers to learn from each other, to initiate and continue collaborations, to communicate recent work, and to further advance the field by making progress on fundamental open problems and developing further connections with other branches of mathematics. We trust that younger mathematicians will greatly contribute to the success of the program with their new ideas. It is our hope that this program will provide a unique opportunity for women and underrepresented groups to make outstanding contributions to the field and we strongly encourage their participation.

    Updated on Feb 27, 2023 03:02 PM PST
  41. Workshop Connections Workshop: Probability and Statistics of Discrete Structures

    Organizers: Christina Goldschmidt (University of Oxford), Po-Ling Loh (University of Cambridge), Kavita Ramanan (Brown University), Dana Randall (Georgia Institute of Technology), LEAD Nike Sun (Massachusetts Institute of Technology)
    Image
    AI-generated interpretation of a random network

    This two-day workshop will bring together researchers from discrete mathematics, probability theory, theoretical computer science, and statistics to explore topics at their interface. The focus will be on probability and statistics of random discrete structures, as well as their applications, including in computer science and physical systems. The workshop will celebrate academic and gender diversity, bringing together women and men at junior and senior levels of their careers from mathematics, physics, and computer science.

    Updated on May 30, 2023 03:32 PM PDT
  42. Workshop Introductory Workshop: Probability and Statistics of Discrete Structures

    Organizers: Louigi Addario-Berry (McGill University), LEAD Shankar Bhamidi (University of North Carolina), Christina Goldschmidt (University of Oxford), Dana Randall (Georgia Institute of Technology), Perla Sousi (University of Cambridge), Remco van der Hofstad (Technische Universiteit Eindhoven)
    Image
    Visualization of a network constructed using simple probabilistic rules, showing the emergence of hubs and other macroscopic network phenomenon. From https://graph-tool.skewed.de

    Networks, graph driven algorithms, and dynamics on graphs such as epidemics, random walks and centrality measures all play a major role, both in our daily lives as well as many scientific and engineering disciplines. This introductory workshop will bring together experts and junior researchers in combinatorics, probability, and statistics to share a broad vision of major challenges and objectives, with a primary focus on models of random graphs and their limits, network inference, dynamic processes on networks and algorithms and optimization on random structures. 

    Updated on May 30, 2023 11:38 AM PDT
  43. Workshop Connections Workshop: Extremal Combinatorics

    Organizers: Julia Boettcher (London School of Economics and Political Science), Anita Liebenau (University of New South Wales), LEAD Maya Stein (Universidad de Chile)
    Logomsriextcomb1

    The purpose of this workshop is to bring together promising early-career researchers in extremal combinatorics who are women or from underrepresented minorities so that they can meet with, forge connections with, and be inspired by the leading figures in the area. The workshop will include lectures, time for collaborative research, and an informal panel discussion session among female and minority researchers on career issues.

    Updated on Apr 04, 2023 08:43 AM PDT
  44. Workshop Introductory Workshop - Graph Theory: Extremal, Probabilistic and Structural

    Organizers: LEAD Penny Haxell (University of Waterloo), Michael Krivelevich (Tel Aviv University), Alex Scott (University of Oxford)
    Logomsriextcomb1

    This workshop will feature leading experts in several major areas of graph theory, including extremal, probabilistic and structural aspects of the field. Introductory lectures will form an important part of the program, providing background and motivation, and aimed at a general mathematical audience. Complementing these, research talks will share exciting recent developments in graph theory.

    Updated on Mar 31, 2023 03:48 PM PDT
  45. Workshop Algebraic and Analytic Methods in Combinatorics

    Organizers: Janos Pach (Alfréd Rényi Institute of Mathematics), Andrew Suk (University of California, San Diego), LEAD Yufei Zhao (Massachusetts Institute of Technology)
    Image
    A degree 7 curve passing through 35 points in the plane

    Many exciting breakthroughs in combinatorics involve innovative applications of techniques from a wide range of areas such as harmonic analysis, polynomial and linear algebraic methods, spectral graph theory, and representation theory. This workshop will present recent developments in this area and facilitate discussions of research problems.

    Updated on Jul 19, 2023 04:10 PM PDT
  46. Workshop Hot Topics: Interactions between Harmonic Analysis, Homogeneous Dynamics, and Number Theory

    Organizers: Dubi Kelmer (Boston College), LEAD Amir Mohammadi (University of California, San Diego), Hong Wang (New York University, Courant Institute)
    Image

    In recent years techniques from harmonic analysis viz. projection theorems have found striking applications in finitary analysis on homogenous spaces. Such quantitative results have many potential applications to analytic number theory. This workshop will bring together researchers in these areas to further explore these connections.

    Updated on Sep 18, 2023 02:09 PM PDT
  47. Workshop Detection, Estimation, and Reconstruction in Networks

    Organizers: Po-Ling Loh (University of Cambridge), Gabor Lugosi (ICREA), Sofia Olhede (École Polytechnique Fédérale de Lausanne (EPFL)), Roberto Oliveira (Institute of Pure and Applied Mathematics (IMPA)), LEAD Miklos Racz (Northwestern University)
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    <p>Recovering communities&nbsp;in&nbsp;a network</p>

    In a growing number of applications, one needs to analyze and interpret data coming from massive networks. The statistical problems arising from such applications lead to important mathematical challenges: building novel probabilistic models, understanding the possibilities and limitations for statistical detection and inference, designing efficient algorithms, and understanding the inherent limitations of fast algorithms. The workshop will bring together leading researchers in combinatorial statistics, machine learning, and random graphs in the hope of cross-fertilization of ideas.

    Updated on Aug 05, 2023 10:06 AM PDT
  48. Program Kinetic theory: Novel statistical, stochastic and analytical methods

    Organizers: Laurent Desvillettes (Université de Paris VII (Denis Diderot)), Irene M. Gamba (University of Texas, Austin), Francois Golze (École Polytechnique), LEAD Pierre Emmanuel Jabin (Pennsylvania State University), Qin Li (University of Wisconsin-Madison), Chiara Saffirio (Universität Basel), Lexing Ying (Stanford University)
    357 image
    Top: Neutrino interactions and neutrino-atom interactions. Bottom: Collision of two "waves"

    The focus of the proposed program is on so-called kinetic equations, describing the evolution of the of many-particle interacting systems. These models have the form of statistical flows, with their solutions being either a single or multiple point probability density functions or measures, supported in a space of attributes. The attributes are problem-dependent and can be molecular velocity, energy, opinion, wealth, and many others. The flow then predicts the evolution of the probability measure in time, position in space, and the interchanging of the particles' states by the transition probability.

    Probably the most classical kinetic equation is the Boltzmann equation which describes the evolutions of the phase-space density function for a dilute gas under binary molecular collisions. Other well-known classical kinetic models include the Landau equation, Vlasov equation for plasmas or other systems, Fokker-Planck equations or kinetic formulations of various macroscopic or hyperbolic systems.

    In recent years, the successes of kinetic theory gave rise to an rapidly increasing variety of mathematical models beyond physics to applications in life sciences, social sciences, economy. Even more recently fascinating connections between kinetic theory and some aspects of data science have emerged.

    Kinetic theory has strong and fascinating interactions with a large variety of other fields, including statistical mechanics, stochastic processes, dynamical systems...

    The program will strive to give an overview of the novel mathematical tools used in kinetic theory through a broad range of classical and more recent applications.

    Updated on Sep 18, 2023 02:50 PM PDT
  49. Program Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups

    Organizers: Martin Bridgeman (Boston College), Richard Canary (University of Michigan), Amir Mohammadi (University of California, San Diego), Hee Oh (Yale University), Maria Beatrice Pozzetti (Ruprecht-Karls-Universität Heidelberg), Jean-François Quint (Université de Bordeaux I)
    Traveler800
    <p>This figure depicts dynamics of flows on convex cocompact hyperbolic 3-manifolds; where the girl is a traveller along a horocycle.</p>

    This research program will bring together two intellectual communities that have made significant advances in the study of discrete subgroups of higher rank semisimple Lie groups: the homogeneous dynamics community and the community studying geometric structures and Anosov groups.

    A discrete subgroup Γ of a semisimple Lie group G may be studied from many different viewpoints. On the one hand, the quotient G/Γ is a homogenous space; through the lens of homogeneous dynamics one can study flows on these spaces, their orbit closures, measure classifications, counting and equidistributions. On the other hand, the group G acts on a plethora of different geometries, including Riemannian and non-Riemannian symmetric spaces, projective spaces and flag manifolds. In many cases, this induces interesting properly discontinuous actions of Γ which can be studied using geometric methods. A flexible class of such discrete subgroups is given by Anosov groups, introduced by Labourie in his study of Hitchin representations and now accepted as the natural higher rank analogue of convex cocompact subgroups of rank one Lie groups. In recent years, their study has made tremendous advances by drawing inspiration from classical Teichmuller theory, and the theory of Kleinian groups.

    When G has rank one, there has already been a fruitful interaction between the two communities, resulting in important advances in understanding the dynamics of the frame flow and unipotent flow on the frame bundle of convex cocompact and geometrically finite hyperbolic manifolds. In turn this had important applications to Apollonian circle packings, Zaremba’s conjecture, expanders, affine sieve problems for thin groups, and related problems, as well as groundberaking work in Teichmuller dynamics.

    Exciting applications of the interaction between homogeneous dynamics and Anosov representations have begun to emerge in recent years, suggesting that now is very promising time to bring together these two communities. The notion of a thin subgroup, inspired from number theory, is one of the many points of convergence. Other recent advances include the study of homogeneous
    dynamics in the setting of Borel Anosov groups, relations between the Hausdorff dimension of limit sets of Anosov groups with counting problems, as well as applications of the thermodynamical formalism in the study of Anosov representations. A strong link between Anosov groups and Hilbert geometry recently opened the door to a very active study of dynamics in these geometries.
    This recent work seems likely to be just the first fruit of the interaction between dynamics and geometry for discrete subgroups of semisimple Lie groups.

    Updated on Sep 19, 2023 12:59 PM PDT
  50. Program Topological and Geometric Structures in Low Dimensions

    Organizers: Ian Agol (University of California, Berkeley), Kenneth Bromberg (University of Utah), Sebastian Hensel (LMU München), Christopher Leininger (Rice University), Kathryn Mann (Cornell University), LEAD Yair Minsky (Yale University), Rachel Roberts (Washington University)
    368 image
    The stable and unstable foliations near a singular orbit of a pseudo- Anosov flow in 3 dimensions. Courtesy Michael Landry.

    Low dimensional topology is a meeting place for ideas, objects and techniques that interact richly with each other, and generate implications for many parts of mathematics. Geometric structures, such as hyperbolic structures on 2- and 3-manifolds, interact with dynamical properties of flows and with analysis on parameter spaces such as the Teichmuller space of a surface or a foliation by surfaces. Combinatorial objects such as complexes of curves and their generalizations give us insight into the behavior of mapping class groups, which encapsulate the topological symmetries of a surface, as well as homeomorphism and diffeomorphism groups which blend topology and dynamics.

    Seminal work of Thurston in the 1970’s brought many of these ideas together in new ways, and inspired multiple lines of work in the time since then, exploring different aspects of the relationship between geometry, topology, analysis and dynamics. Recent progress in these fields has taken each in new directions, suggesting that refocusing on their interactions will yield dividends towards progress on key problems within this central area and grow outwards towards its many connections with other areas of mathematics.

    As examples of structural questions in the overlap of these areas: How do we classify Anosov and pseudo-Anosov flows on 3-manifolds up to orbit equivalence? Can we relate the dynamics of pseudo-Anosov flows on hyperbolic 3-manifolds to the geometry of the underlying 3-manifolds? Can we relate the leafwise Teichmuller theory of a foliation to geometric structures on the underlying 3-manifold? How well can we understand the subgroup structure of homeomorphism and diffeomorphism groups of surfaces? Can mapping class groups of infinite-type surfaces be harnessed to study dynamical questions?

    The program will bring together experts in all these fields and younger researchers, who together can address these sorts of questions and open new areas for exploration. 

    Updated on Sep 19, 2023 12:49 PM PDT

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