
Program Complementary Program 202324
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 
MSRIUP MSRIUP 2024: Mathematical Endocrinology
Organizers: Alexander DiazLopez (Villanova University), Maria Mercedes Franco (Queensborough Community College (CUNY)), Rebecca Garcia (Colorado College), LEAD Candice Price (Smith College), Robin Wilson (Loyola Marymount University)The MSRIUP summer program is designed to serve a diverse group of undergraduate students who would like to conduct research in the mathematical sciences.
In 2024, MSRIUP 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 Mar 07, 2024 11:11 AM PST 
Program Quantum Symmetries Reunion
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 Galoislike 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 Jun 27, 2024 12:12 PM PDT 
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)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 Mar 19, 2024 04:24 PM PDT 
Seminar Quantum Symmetries on noncommutative tori
Updated on Jul 18, 2024 08:54 AM PDT 
Seminar Subfactors and quantum symmetries
Updated on Jul 18, 2024 10:57 AM PDT

Seminar A braided tensor 2category from link homology
Updated on Jul 19, 2024 12:04 PM PDT 
Seminar Integrability from Categories?
Updated on Jul 19, 2024 07:55 AM PDT 
Seminar Lecture
Created on Jul 22, 2024 11:00 AM PDT 
Seminar On algebraisation of lowdimensional Topology
Updated on Jul 19, 2024 11:30 AM PDT 
Seminar Deformations of tensor categories generated by one object
Updated on Jul 22, 2024 07:54 AM PDT 
Seminar Quantum Apolynomials and cluster quantization
Updated on Jul 19, 2024 09:54 AM PDT 
Summer Graduate School Multigraded and differential graded methods in commutative algebra (St. Mary's College)
Organizers: Michael Brown (Auburn University), Claudia Miller (Syracuse University)This summer graduate school focuses on modern homological techniques in commutative algebra, specifically those involving multigraded and differential graded structures. These topics have a long and rich history, but neither is generally covered in graduate courses. Moreover, recent developments have exhibited exciting interplay between the two subjects.
The purpose of the school is to introduce the participants to modern themes on these topics, including Koszul duality for toric varieties and differential graded algebra structures on resolutions. The school will consist of two lectures each day and carefully planned problem sessions designed to reinforce the foundational material, with an emphasis on using computational tools such as the symbolic algebra program Macaulay2.
Updated on Jul 16, 2024 09:17 AM PDT 
Summer Graduate School Analysis of Partial Differential Equations (Okinawa Institute of Science and Technology)
Organizers: Ugur Abdulla (Okinawa Institute of Science and Technology), GuiQiang Chen (University of Oxford)This two week summer school, jointly organized by SLMath with OIST, will offer the following two minicourses:
 Measuretheoretical analysis, divergencemeasure fields, and nonlinear PDEs of divergence form
This course will present some recent developments in the theory of divergencemeasure fields via measuretheoretic analysis and its applications to the analysis of nonlinear PDEs of conservative form – nonlinear conservation laws.  Perron’s method and Wienertype 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 May 24, 2024 09:32 PM PDT  Measuretheoretical analysis, divergencemeasure fields, and nonlinear PDEs of divergence form

Seminar Lightning Talks
Updated on Jul 10, 2024 10:49 AM PDT 
Seminar Lecture
Updated on Jul 10, 2024 11:04 AM PDT 
Seminar Lecture
Updated on Jul 10, 2024 11:09 AM PDT 
Seminar Lecture
Updated on Jul 10, 2024 11:12 AM PDT 
Seminar Lecture
Updated on Jul 10, 2024 11:32 AM PDT 
Seminar Lecture
Updated on Jul 10, 2024 11:44 AM PDT 
Seminar Lecture
Updated on Jul 15, 2024 10:22 AM PDT 
Summer Graduate School Mathematical Spin Glass Theory (Courant, NY)
Organizers: Antonio Auffinger (Northwestern University), WeiKuo Chen (University of Minnesota), LEAD Eliran Subag (Weizmann Institute of Science)While their original aim was to explain the strange behavior of certain magnetic alloys, the study of spin glass models has led to a farreaching 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 meanfield 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 superlevel 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 and ideas that were developed to obtain them, as well as exposing the students to some recent research topics.
Updated on Apr 19, 2024 03:00 PM PDT 
Seminar Lecture
Updated on Jul 10, 2024 12:52 PM PDT 
Seminar Lecture
Updated on Jul 10, 2024 01:02 PM PDT 
Seminar Lecture
Updated on Jul 10, 2024 01:13 PM PDT 
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Updated on Jul 10, 2024 01:15 PM PDT 
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Updated on Jul 22, 2024 08:43 AM PDT 
Program New Frontiers in Curvature: Flows, General Relativity, Minimal Submanifolds, and Symmetry
Organizers: LEAD Ailana Fraser (University of British Columbia), LanHsuan Huang (University of Connecticut), Richard Schoen (Stanford University), LEAD Catherine Searle (Wichita State University), Lu Wang (Yale University), Guofang Wei (University of California, Santa Barbara)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 
Program Special Geometric Structures and Analysis
Organizers: Eleonora Di Nezza (Institut de Mathématiques de Jussieu; École Normale Supérieure), LEAD Mark Haskins (Duke University), Tristan Riviere (ETH Zurich), Song Sun (Zhejiang University; University of California, Berkeley), Xuwen Zhu (Northeastern University)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 
Program Complementary Program 202425
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 
Workshop Connections Workshop: New Frontiers in Curvature & Special Geometric Structures and Analysis
Organizers: SunYung Chang (Princeton University), LanHsuan Huang (University of Connecticut), Chikako Mese (Johns Hopkins University), Ilaria Mondello (Université ParisEst Créteil ValdeMarne), LEAD Guofang Wei (University of California, Santa Barbara), LEAD Xuwen Zhu (Northeastern University)This threeday workshop will consist of various talks given by prominent women mathematicians on topics of differential geometry and geometric analysis. These will be appropriate for graduate students, postdocs, and researchers in areas related to the two Fall 2024 programs at SLMath. The workshop will also include activities to promote interaction and connection between participants. This workshop is open to all mathematicians.
Updated on Jun 11, 2024 01:48 PM PDT 
Workshop Introductory Workshop: New Frontiers in Curvature
Organizers: Ailana Fraser (University of British Columbia), Karsten Grove (University of Notre Dame), Richard Schoen (Stanford University), Catherine Searle (Wichita State University), LEAD Lu Wang (Yale University)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 semiexpository lectures on recent advances and breakthroughs involving interactions between the four main topics. This will set the stage and provide important context for the semesterlong program itself.
Updated on Jun 24, 2024 09:32 AM PDT 
Workshop Introductory Workshop: Special Geometric Structures and Analysis
Organizers: Anda Degeratu (Universität Stuttgart), LEAD Eleonora Di Nezza (Institut de Mathématiques de Jussieu; École Normale Supérieure), Luca Spolaor (University of California, San Diego), Song Sun (Zhejiang University; University of California, Berkeley)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 13, 2024 09:15 AM PDT 
Workshop Recent progress on geometric analysis and Riemannian geometry
Organizers: LEAD LanHsuan Huang (University of Connecticut), Andre Neves (University of Chicago), Richard Schoen (Stanford University), LEAD Catherine Searle (Wichita State University), Guofang Wei (University of California, Santa Barbara)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 Jul 16, 2024 03:05 PM PDT 
Workshop Geometry and analysis of special structures on manifolds
Organizers: Anna Fino (Università di Torino; Florida International University), Mark Haskins (Duke University), Tristan Riviere (ETH Zurich), Neshan Wickramasekera (University of Cambridge)The analysis of solutions to nonlinear geometric PDEs with higherdimensional singular sets has seen some notable recent advances, but many fundamental questions still remain open. This workshop will bring together a wide array of researchers working in differential geometry, gauge theory, nonlinear PDEs, microlocal analysis, the calculus of variations and geometric measure theory, with the goal of describing recent advances, advertising recent technical breakthroughs and forging new connections.
Updated on Apr 30, 2024 11:08 AM PDT 
Workshop Hot Topics: Life after the Telescope Conjecture
Organizers: LEAD Agnes Beaudry (University of Colorado), Michael Hill (University of California, Los Angeles), Vesna Stojanoska (University of Illinois at UrbanaChampaign)In June 2023, Burklund, Hahn, Levy, and Schlank surprised the homotopy theory community when they announced a disproof of Ravenel's Telescope Conjecture, a fundamental problem of homotopy theory which had been open for 40 years and was believed to be out of reach. The disproof of the Telescope Conjecture combines some of the most exciting recent developments in homotopy theory. This includes fundamental work on redshift phenomena and descent in algebraic Ktheory, trace methods based on a novel approach to topological Hochschild and cyclic homology, ambidexterity in chromatic homotopy theory, and more.
The workshop will explore this amazing body of work, culminating in its synthesis and ingenious application to disprove the Telescope Conjecture.
Updated on Apr 30, 2024 11:09 AM PDT 
Program Probability and Statistics of Discrete Structures
Organizers: Louigi AddarioBerry (McGill University), Christina Goldschmidt (University of Oxford), PoLing Loh (University of Cambridge), Gabor Lugosi (ICREA), Dana Randall (Georgia Institute of Technology), LEAD Remco van der Hofstad (Technische Universiteit Eindhoven)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 Feb 29, 2024 02:57 PM PST 
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)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.
Updated on Feb 29, 2024 02:56 PM PST 
Workshop Connections Workshop: Probability and Statistics of Discrete Structures
Organizers: Christina Goldschmidt (University of Oxford), PoLing Loh (University of Cambridge), Kavita Ramanan (Brown University), Dana Randall (Georgia Institute of Technology), LEAD Nike Sun (Massachusetts Institute of Technology)This twoday 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 
Workshop Introductory Workshop: Probability and Statistics of Discrete Structures
Organizers: Louigi AddarioBerry (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)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 
Workshop Connections Workshop: Extremal Combinatorics
Organizers: Julia Böttcher (London School of Economics and Political Science), Anita Liebenau (University of New South Wales), LEAD Maya Stein (Universidad de Chile)The purpose of this workshop is to bring together promising earlycareer 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 
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)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 
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 (Massachusetts Institute of Technology)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 Apr 12, 2024 09:01 AM PDT 
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)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 
Workshop Detection, Estimation, and Reconstruction in Networks
Organizers: PoLing 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)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 crossfertilization of ideas.
Updated on Aug 05, 2023 10:06 AM PDT 
Summer Graduate School Séminaire de Mathématiques Supérieures 2025: An Introduction to Recent Trends in Commutative Algebra (Toronto, Canada)
Organizers: Sergio Da Silva (Virginia State University), Federico Galetto (Cleveland State University), Elena Guardo (Università di Catania), Megumi Harada (McMaster University), Patricia Klein (Texas A & M University), Jenna Rajchgot (McMaster University), Adam Van Tuyl (McMaster University)The 2025 SMS will allow graduate students to learn about a number of recent trends and advances in the field of commutative algebra. The aim of the SMS is to provide an “onramp” for graduate students interested in algebra, combinatorics, and/or algebraic combinatorics to learn more about commutative algebra’s interaction with these fields. The introductory courses will introduce fundamental skills in commutative algebra, the more intermediate courses will expose students to cuttingedge research in the field. The school will focus on four topics within commutative algebra: Combinatorial Methods, Homological Methods, Computational Methods, and Characteristic p Methods. The SMS will provide both a series of introductory lectures and intermediate/advanced lectures from leaders in one of the four areas. The lectures will include a series of problem sessions that will allow participants to develop and hone their skills in these areas, which will be especially helpful for new people to the field. Participants will be encouraged to work collaboratively, both to enhance their own mathematical networks as well as to promote future collaborations beyond the school.
Updated on Jul 08, 2024 03:12 PM PDT 
Summer Graduate School Local Limits of Random Graphs (ParisSaclay University, France)
Organizers: Ainhoa AparicioMonforte (Fondation Mathématique Jacques Hadamard (FMJH)), Alexandra Genesco (Fondation Mathématique Jacques Hadamard (FMJH)), LEAD Pascal Massart (Fondation Mathématique Jacques Hadamard (FMJH))Random graphs are ubiquitous in modern probability theory. Besides their intrinsic mathematical beauty, they are also used to model complex networks. In the early 2000’s, I. Benjamini and O. Schramm introduced a mathematical framework in which they endowed the set of locally finite rooted connected graphs with the structure of a Polish space, called the local topology. The goal of this summer school is to introduce the framework of local limits of random graphs, the concepts of BenjaminiSchramm (or unbiased) limits and unimodularity, as well as the most important applications. The lectures will be delivered by Nicolas Curien (Prof. ParisSaclay University) and Justin Salez (Prof. Université ParisDauphine) and will be complemented by many problem sessions, where students will work in small groups under the guidance of teaching assistants, who are researchers in the field.
Updated on Jul 12, 2024 01:18 PM PDT 
Summer Graduate School 2025 PIMSCRM Summer School in Probability (Vancouver, Canada)
Organizers: Louigi AddarioBerry (McGill University), Omer Angel (University of British Columbia), Mathav Murugan (University of British Columbia), Gordon Slade (University of British Columbia)The Summer Schools in Probability are a highlight of Canadian probability and are internationally significant. Launched by PIMS in 2004, the school takes the form of two main 4week courses along with three minicourses. The schools have played a major role in the development of an exceptionally strong community of young probabilist in Canada, North America and overseas. This will be the 13th time this school has run.
Updated on Mar 22, 2024 01:06 PM PDT 
Summer Graduate School Statistical Optimal Transport (St. Mary's College)
Organizers: LEAD Promit Ghosal (Brandeis University), Jonathan NilesWeed (New York University, Courant Institute), Marcel Nutz (Columbia University)This summer school offers an exceptional opportunity for participants to delve into the intricate realm of statistical optimal transport theory. This captivating field stands at the crossroads of multiple disciplines, drawing from a rich tapestry of mathematical insights from diverse subjects, including partial differential equations, stochastic analysis, convex geometry, statistics, and machine learning, crafting a vibrant and interdisciplinary landscape. The foremost objective of this summer school is to create a dynamic learning environment that unites students from diverse backgrounds such as PDE theory, probability, or optimal transport.
Updated on Mar 20, 2024 02:04 PM PDT 
African Diaspora Joint Mathematics ADJOINT 2025
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 twoweek summer session for ADJOINT 2025 will take place June 1627, 2025 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 SelfADJOINT as part of an existing or newlyformed 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 May 22, 2024 10:52 AM PDT 
Summer Graduate School New Perspectives on Discriminants and Applications (Max Planck, Leipzig)
Organizers: Eliana Duarte (Centro de Matemática da Universidade do Porto), Serkan Hosten (San Francisco State University), Simon Telen (MaxPlanckInstitut)This summer school will offer a handson introduction to discriminants, with a view towards modern applications. Starting from the basics of computational algebraic geometry and toric geometry, the school will gently introduce participants to the foundations of discriminants. A particular emphasis will be put on computing discriminants of polynomial systems using computer algebra software. Then, we will dive into three applications of discriminants: algebraic statistics, geometric modeling, and particle physics. Here, discriminants contribute to the study of maximum likelihood estimation, to finding practical parametrizations of geometric objects, and to computations of scattering amplitudes. We will explain recently discovered unexpected connections between these three applications. In addition to lectures, the summer school will have daily collaborative exercise sessions which will be guided by the teaching assistants and will include software demonstrations.
Updated on Jul 16, 2024 11:50 AM PDT 
Summer Graduate School Graphical Models in Algebraic Combinatorics (St. Mary's College)
Organizers: Christian Gaetz (University of California, Berkeley), David Keating (University of Illinois at UrbanaChampaign), Melissa ShermanBennett (University of California, Davis), LEAD Anna Weigandt (University of Minnesota)This school will introduce students to a range of powerful combinatorial tools used to understand algebraic objects ranging from the homogeneous coordinate ring of the Grassmannian to symmetric functions. The summer school will center around two main lecture series "Webs and Plabic Graphs" and "Vertex Models and Applications". While the exact applications differ, both courses will center on graphical models for algebraic problems closely related to Grassmannian and its generalizations. This school will be accessible to a wide range of students. Students will leave the school with a solid grasp of the combinatorics of webs, plabic graphs, and the sixvertex model, an understanding of their algebraic applications, and a taste of current research directions.
Updated on Jul 08, 2024 03:09 PM PDT 
Summer Graduate School Noncommutative Algebraic Geometry (Antwerp, Belgium)
Organizers: Pieter Belmans (University of Luxembourg), Lander Hermans (Universiteit Antwerp), Wendy Lowen (Universiteit Antwerpen), Arne Mertens (Universiteit Antwerp), Michel VAN DEN BERGH (Hasselt University), Špela Špenko (Université Libre de Bruxelles)This two week school on Noncommutative Algebraic Geomery will be held at the University of Antwerp in Belgium. The school will consist of two courses: Homological Mirror Symmetry and Algebraic Models for Spaces. These courses will be planned and taught by organisers with the help of teaching assistants for the problem sessions. The school will be aimed at a wide range of graduate students, from students with a Bachelor degree to beginning PhD students. The lectures and problem sessions will be complemented by a poster session in week one and a total of four introductory research talks on Friday afternoons.
Updated on Jul 11, 2024 02:59 PM PDT 
Summer Graduate School Computer Assisted Proofs in Applied Mathematics (SLMath)
Organizers: LEAD Jonathan Jaquette (New Jersey Institute of Technology), Evelyn Sander (George Mason University)One of the core elements of applied mathematics is mathematical modeling consisting of nonlinear equations such as ODEs, and PDEs. A fundamental difficulty which arises is that most nonlinear models cannot be solved in closed form. Computer assisted proofs are at the forefront of modern mathematics and have led to many important recent mathematical advances. They provide a way of melding analytical techniques with numerical methods, in order to provide rigorous statements for mathematical models that could not be treated by either method alone. In this summer school, students will review standard computational and analytical techniques, learn to combine these techniques with more specialized methods of interval arithmetic, and apply these methods to establish rigorous results in otherwise intractable problems
Updated on Apr 08, 2024 08:55 AM PDT 
Summer Graduate School Principled Scientific Discovery with Formal Methods (IBM, Yorktown)
Organizers: Chid Apte (IBM Thomas J. Watson Research Center), Sanjeeb Dash (IBM Thomas J. Watson Research Center), Lior Horesh (IBM Thomas J. Watson Research Center)The summer school aims to expose participants to formal methods that can facilitate principled scientific discovery. The school will cover some of the basic automated statistical inference (in the form of machine learning techniques) and reasoning methods that are commonly used in scientific discovery, as well as novel techniques developed to tackle open questions and issues. This summer school will address novel computational methods for scientific discovery and focus on fusing axiomatic knowledge and experimental data to enable principled derivations of models of natural phenomena along with certificates of the consistency of these models with background knowledge specified as axioms.
Updated on Jul 12, 2024 10:34 AM PDT 
Summer Graduate School Geometry and Dynamics in Higher Rank Lie Groups (St. Mary's College)
Organizers: Richard Canary (University of Michigan), Sara Maloni (University of Virginia), Wenyu Pan (University of Toronto), Cagri Sert (University of Zurich), LEAD Tengren Zhang (National University of Singapore)Lie groups are central objects in modern mathematics; they arise as the automorphism groups of many homogeneous spaces, such as flag manifolds and Riemannian symmetric spaces. Often, one can construct manifolds locally modelled on these homogeneous spaces by taking quotients of their subsets by discrete subgroups of their automorphism groups. Studying such discrete subgroups of Lie groups is an active and growing area of mathematical research. The objective of this summer school is to introduce young researchers to a class of discrete subgroups of Lie groups, called Anosov subgroups.
Updated on Apr 18, 2024 08:43 AM PDT 
Summer Graduate School Topological and Geometric Structures in Low Dimensions (SLMath)
Organizers: LEAD Kenneth Bromberg (University of Utah), Kathryn Mann (Cornell University)This school will serve as an introduction to the SLMath semester “Topological and Geometric Structures in LowDimensions”. The school consists of two minicourses: one on Teichmüller Theory and Hyperbolic 3Manifolds and the other on Anosov Flows on Geometric 3Manifolds. Both topics lie at the interface of lowdimensional geometric topology (specifically, surfaces, foliations, and 3manifolds) and lowdimensional dynamics. The first course will be targeted towards students who have completed the standard first year graduate courses in geometry, topology, and analysis while the second course will geared towards more advanced students who are closer to beginning research. However, we expect that all students will benefit from both courses.
Updated on Mar 21, 2024 09:48 AM PDT 
Program Kinetic Theory: Novel Statistical, Stochastic and Analytical Methods
Organizers: Laurent Desvillettes (Université Paris Cité), Irene M. Gamba (University of Texas, Austin), Francois Golze (École Polytechnique), LEAD Pierre Emmanuel Jabin (Pennsylvania State University), Qin Li (University of WisconsinMadison), Chiara Saffirio (Universität Basel), Lexing Ying (Stanford University)The focus of the proposed program is on socalled kinetic equations, describing the evolution of the of manyparticle 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 problemdependent 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.
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 Apr 17, 2024 08:58 AM PDT 
Program Recent Trends in Stochastic Partial Differential Equations
Organizers: Sandra Cerrai (University of Maryland), Yu Gu (University of Maryland), Massimiliano Gubinelli (University of Oxford), Davar Khoshnevisan (University of Utah), Andrea Nahmod (University of Massachusetts, Amherst), Hao Shen (University of WisconsinMadison), LEAD Lorenzo Zambotti (Sorbonne Université)The topic Singular Stochastic Partial Differential Equations (singular SPDE) has rapidly grown to be an active research area at the interface of Stochastic Analysis and PDEs on one hand, and Mathematical Physics on the other hand. During this decade we have witnessed a series of tremendous breakthroughs in the solution theories of SPDEs, universality problems, largescale asymptotic behaviors of solutions, and foundational relations with quantum field theories and geometry. Many longstanding problems have been resolved via newly developed methods – notably the theories of regularity structures and paracontrolled distributions – and deep connections with other fields are quickly emerging.
It is a natural time to convene a largescale semester program.
Updated on Jul 09, 2024 04:18 PM PDT 
Program Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups
Organizers: Martin Bridgeman (Boston College), LEAD Richard Canary (University of Michigan), Amir Mohammadi (University of California, San Diego), LEAD Hee Oh (Yale University), Maria Beatrice Pozzetti (RuprechtKarlsUniversität Heidelberg), JeanFrançois Quint (CNRS  Université de Montpellier)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.
Updated on Apr 17, 2024 11:08 AM PDT 
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 in St. Louis)Low dimensional topology is a meeting place for many objects and ideas from diverse areas of mathematics, including foliation theory, geometry, and smooth and conformal dynamics. For instance, many foliations on 3manifolds admit transverse flows, connecting (local) leafwise homeomorphisms to flow dynamics and the mapping class groups of the leaves. Leafwise conformal or hyperbolic structures can be approached through Teichmüller theory, and connect again to onedimensional dynamics through "universal circles" organizing compactifications of all the leaves or of the flow space. Many of these ideas originate in work of Thurston but in recent years have diverged and are ripe for reconnection.
The program will bring together experts in all these fields together with younger researchers, who together can form new connections and open new areas for exploration.Updated on Jul 09, 2024 04:16 PM PDT 
Workshop Recent progress in topological and geometric structures in low dimensions
Organizers: Kenneth Bromberg (University of Utah), Sergio Fenley (Florida State University), Richard Kent (University of WisconsinMadison), LEAD Kathryn Mann (Cornell University), Kasra Rafi (University of Toronto)This workshop will bring together ideas from diverse areas of mathematics that meet in the setting of geometry and topology in low dimensions. This includes the study of flows, foliations, and fibrations of threemanifolds and the related study of geometry (e.g. hyperbolic or conformal structures) of the manifolds and of the leaves or fibers, and their mapping class groups. This is a rich and interconnected area and many adjacent topics will also be featured.
Created on Jul 22, 2024 11:35 AM PDT 
Program Motivic homotopy theory: connections and applications
Organizers: Aravind Asok (University of Southern California), Adrien Dubouloz (Institut de Mathématiques de Bourgogne), Elden Elmanto (University of Toronto, Scarborough; Harvard University), Daniel Isaksen (Wayne State University), PaulArne Ostvaer (Università di Milano), Anand Sawant (Tata Institute of Fundamental Research), Kirsten Wickelgren (Duke University), Maria Yakerson (University of Oxford)Created on May 20, 2024 03:08 PM PDT 
Program New Trends in Tropical Geometry
Organizers: Pierrick Bousseau (University of Georgia), Melody Chan (Brown University), Ilia Itenberg (Institut de Mathématiques de Jussieu  Paris Rive Gauche), Hannah Markwig (EberhardKarlsUniversität Tübingen), LEAD Kris Shaw (University of Oslo)Tropical geometry can be viewed as a degenerate version of algebraic geometry,where the role of algebraic varieties is played by certain polyhedral complexes. As the degeneration process, called tropicalization, preserves many fundamental properties, tropical geometry provides important bridges and an exchange of methods between algebraic geometry, symplectic geometry and convex geometry; these links have been extremely fruitful and gave rise to remarkable results during the last 20 years. The main focus of the program will be on the most significant recent developments in tropical geometry and its applications. The following topics are particularly influential in the area and will be central in the program:
 real aspects of tropical geometry;
 tropical mirror symmetry and nonArchimedean geometry;
 tropical phenomena in symplectic geometry;
 matroids, combinatorial and algebraic aspects;
 tropical moduli spaces;
 tropical geometry and A1homotopy theory.
Updated on Mar 13, 2024 02:34 PM PDT 
Program Inverse Problems and Applications
Organizers: Fioralba Cakoni (Rutgers University), Maarten de Hoop (Rice University), Anna Gilbert (Yale University), Katya Krupchyk (University of California, Irvine), Matti Lassas (University of Helsinki), LEAD Gunther Uhlmann (University of Washington)Inverse problems (IP) arise in all fields of science and technology where a cause for an observed or desired effect is sought. In the last 50 years or so there has been substantial progress in the mathematical understanding of these problems but many questions remain open. The mathematics of these problems involves many areas in Mathematics including PDE, differential geometry, integral geometry, probability, statistics, complex analysis, numerical analysis, mathematical physics, data science, etc. Since the 2010 program at the thenMathematical Sciences Research Institute (now Simons Laufer Mathematical Sciences Institute), there has been significant progress in inverse problems; many of the advances can be traced back to that program. However, there are still deep open questions remaining as well, some of which are discussed in this proposal. New research topics include the connection between IP and machine learning, IP for nonlinear equations, IP for nonlocal operators, and connections between statistics and IP.
Updated on Feb 28, 2024 03:01 PM PST
Past Scientific Events

Seminar Lecture: "An efficient* classical algorithm for TambaraYamagami statesum invariants of 3manifolds"
Updated on Jul 10, 2024 08:52 AM PDT 
Seminar Lecture: "Continuous quantum symmetries"
Updated on Jul 09, 2024 02:05 PM PDT 
Seminar Lecture
Updated on Jul 15, 2024 08:20 AM PDT 
Seminar Lecture
Updated on Jul 09, 2024 01:18 PM PDT 
Seminar Lecture
Updated on Jul 09, 2024 01:20 PM PDT 
Seminar Lightning Talks
Updated on Jul 10, 2024 10:46 AM PDT 
Seminar Lecture
Updated on Jul 09, 2024 01:00 PM PDT 
Seminar Welcome to SLMath
Updated on Jul 11, 2024 11:24 AM PDT 
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)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:
 moduli spaces of stable curves
 Brill–Noether theory
 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 Jul 17, 2024 03:37 PM PDT 
Summer Graduate School Stochastic Quantization (SLMath)
Organizers: Massimiliano Gubinelli (University of Oxford), Martina Hofmanova (Universität Bielefeld), LEAD Hao Shen (University of WisconsinMadison), Lorenzo Zambotti (Sorbonne Université)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 cuttingedge problems of Euclidean quantum field theory.
Updated on Jul 01, 2024 03:11 PM PDT 
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 British Columbia)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 Jul 11, 2024 10:27 AM PDT 
Summer Graduate School Hprinciple (Sendai, Japan)
Organizers: Emmy Murphy (Princeton University), Takashi Tsuboi (RIKEN Interdisciplinary Theoretical and Mathematical Sciences Program)This two week summer school, jointly organized by SLMath with RIKEN, will introduce graduate students to the theory of hprinciples. After building up the theory from basic smooth topology, we will focus on more recent developments of the theory, particularly applications to symplectic and contact geometry, fluid dynamics, and foliation theory.
hprinciples 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 Apr 17, 2024 10:55 AM PDT 
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 twoweek 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 SelfADJOINT as part of an existing or newlyformed 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 Apr 10, 2024 10:50 AM PDT 
Summer Graduate School Introduction to QuantumSafe Cryptography (IBM Zurich)
Organizers: Jonathan Bootle (IBM Zürich Research Laboratory), Luca De Feo (IBM Zürich Research Laboratory)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 quantumsafe cryptosystems. Each week will be dedicated to two of the four families of quantumsafe schemes.
Updated on Jul 11, 2024 09:31 AM PDT 
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; École Normale Supérieure), Song Sun (Zhejiang University; University of California, Berkeley)This summer school will serve as an introduction to the SLMath program "Special geometric structures and analysis". There will be two minicourses: 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 Jun 27, 2024 01:13 PM PDT 
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 WisconsinMadison), Chiara Saffirio (Universität Basel)This summer school will focus on the introductory notions related to the passage of Newtonian and quantum manybody 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 higherlevel 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 Jun 24, 2024 03:48 PM PDT 
Summer Research in Mathematics 2024 Summer Research in Mathematics
MSRI/SLMath's Summer Research in Mathematics program provides space, funding, and the opportunity for inperson collaboration to small groups of mathematicians, especially women and genderexpansive 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 May 21, 2024 03:45 PM PDT 
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; École Normale Supérieure), 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)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 YauTianDonaldson conjecture. The second week will focus on geometric flows in Riemannian and complex geometry.
Updated on Mar 18, 2024 02:15 PM PDT 
Workshop Macaulay2, Computational Algebraic Geometry and String Theory
Organizers: David Eisenbud (University of California, Berkeley), Daniel Grayson, Anton Leykin (Georgia Institute of Technology), Andre Lukas (University of Oxford), Devlin Mallory (University of Utah), Liam McAllister (Cornell University), Karl Schwede (University of Utah), Michael Stillman (Cornell University)Updated on Apr 11, 2024 01:36 PM PDT 
Seminar COMA Seminar: "Methods to Extend the Classical Multiplicities to General Ideals"
Updated on May 16, 2024 01:58 PM PDT 
Seminar COMA Colloquium: "Towards an analogue of Fsignature functions in mixed characteristic"
Updated on May 16, 2024 08:18 AM PDT 
Seminar COMA Working Group: Syzygies: "Minimal Resolutions and the Homology of Matching and Chessboard Complexes, by Victor Reiner and Joel Roberts"
Updated on May 16, 2024 01:56 PM PDT 
Seminar "COMA Working Group: ""A second look at parasolid closure"" "
Updated on May 17, 2024 11:51 AM PDT 
Seminar COMA Special Topic: Mixed characteristic analogues of Finjective and Du Bois singularities"
Updated on May 15, 2024 12:37 PM PDT 
Seminar COMA/NAG Joint Graduate Student Seminar: "Factoriality of LSS ideals"
Updated on May 13, 2024 08:13 AM PDT 
Seminar COMA Colloquium: "Koszul Binomial Edge Ideals"
Updated on May 13, 2024 08:27 AM PDT