<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.

The analysis of solutions to nonlinear geometric PDEs with higher-dimensional 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.

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 red-shift phenomena and descent in algebraic K-theory, 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.

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.

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. 

This workshop will bring together promising early-career researchers in extremal combinatorics 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 on career issues. This workshop is open to all mathematicians.

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.

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.

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.

Activist Bob Moses argued that mathematical literacy was the next civil rights front line. The 2025 CIME workshop will explore what mathematical literacy might mean and why it still matters for citizenship now and in the future. The workshop’s long-term impact relies on the participation of research mathematicians, mathematics educators, educational researchers, teachers of school mathematics, and policymakers working across different perspectives and roles to foster collaboration that will raise the floor for mathematical literacy for citizenship now and in the future.

This is an exciting time for mathematics, as new technologies for mathematical reasoning provide novel opportunities for mathematical research, communication, and discovery. Mathlib, a library of formal mathematics, now contains one-and-a-half million lines of code. Important results like the proof of polynomial Freiman-Ruzsa conjecture by Gowers, Green, Manners, and Tao and the exponential improvement to the upper bound on Ramsey's theorem by Campos, Griffiths, Morris, and Sahasrabudhe were formally verified in the Lean proof assistant even before they were accepted to journals. Open problems in combinatorics have been solved with the help of automated reasoning, and AI introduced by Deepmind was deemed to have performed at the level of a silver medalist at the most recent International Mathematical Olympiad.

This workshop will introduce mathematicians and theoretical computer scientists to the technologies that underlie these recent successes, namely, proof assistants, automated reasoning, and machine learning. Talks each morning will survey exciting results in the field, and in the afternoons, we will help participants experiment with the tools to get a sense of what they do. We will also encourage participants to think about how they can use the new technologies in their research.

Recovering communities in a network.

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.

The overarching goal of the 2025 Workshop on Mathematics and Racial Justice is to extend our explorations of how the mathematical sciences plays a central role in today's movement for racial justice. We will examine the various systems identified in the 2021 Math and Racial Justice workshop and consider the impact of these systems on BIPOC (Black, Indigenous, and people of color) communities.  This workshop defines racial justice as the result of intentional, active and sustained anti-racist practices that identify and dismantle racist structures and policies that operate to oppress, disenfranchise, harm, and devalue BIPOC people. This workshop will bring together mathematicians, statisticians, computer scientists, STEM educators, and members of the general public interested in using the tools of these disciplines to critically examine and eradicate racial disparities in society. Researchers with expertise or interest in problems at the intersection of the mathematical sciences and racial justice are strongly encouraged to participate. Thanks to funding from the Mathematical Sciences Institutes Diversity Initiative, there is financial support available for a limited number of attendees. This in-person workshop will take place over three days, May 7-9, 2025, at SLMath in Berkeley, CA. The themes for this year’s workshop are 1) developing racial literacy, 2) science and technology studies, 3) law and policy, and 4) education.

The Connections workshop will bring together leading experts working at the intersection of kinetic theory and stochastic partial differential equations (SPDEs).

Parameter scan for deploying external electric field to control two-stream instability for Vlasov-Poisson.

The goal of the workshop is to introduce non-experts to two active research areas: kinetic theory and stochastic partial differential equations. Kinetic theory studies the properties of interacting particle systems modeling various processes in non-equilibrium statistical mechanics. Stochastic partial differential equations describe dynamics subjected to random noises. The methods from the two areas complement each other in studies of the phenomena arising in physics, economics, life sciences, etc.

The motion of a random string.

The workshop aims to bring together researchers working on different facets of stochastic PDEs. The field of stochastic PDEs has seen many new techniques recently appear to tackle different problems, including renormalization, large scale and long-time behaviours, stochastic fluid dynamics, and homogenization. The goal of the workshop is to facilitate discussions and allow different communities to engage with one another one.

Infinite-dimensional division algebras are essential in noncommutative algebra and noncommutative algebraic geometry, yet they have remained cryptic and largely unclassified. This workshop will address three key classical open problems concerning them: the Kurosh Problem, the Free Subalgebra Problem and Artin's Conjecture. We will review decades of progress on these wide-open problems and emphasize novel techniques and emerging theories and concepts that show promise in facilitating breakthroughs.

The joint introductory workshop for the programs in Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups and Topological and Geometric Structures in Low Dimensions will feature lectures introducing subjects of interest to both programs, including Teichmuller Theory, geometry in higher rank, foliations and flows, Anosov groups and thermodynamic formalism,  mapping class groups, counting and equidistribution, and related topics. Minicourses will be targeted at early career researchers as well as specialists looking to find connections between the different subjects.

Foliations around a pseudo-Anosov singularity (Image credit: Chi Cheuk Tsang)

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 three-manifolds 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.

Limit set of an Anosov representation

This workshop will focus on recent advances on geometric and dynamical approaches to the study of discrete subgroups of higher rank Lie groups and their deformation spaces. The goal will be to present results and exchange ideas from different areas of mathematics, and we hope to create bonds between several different mathematical communities.