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 led 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.

Mathematics is often viewed as one of the main tools responsible for scientific progress, and developments in mathematics are behind some of society’s most significant technological advancements. More recently, mathematicians have increasingly been addressing issues of quantitative justice in their research, their teaching, and their institutions. Quantitative justice is a field that uses the tools of mathematics to interrogate and address the inequities faced by marginalized communities. This workshop is a part of that movement and 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 address fairness and disparities in society.

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.

Top: Neutrino interactions and neutrino-atom interactions. Bottom: Collision of two "waves"

This workshop will explore the latest advances in kinetic theory and stochastic particle dynamics in mean field regimes, covering both classical themes and emerging areas. Topics will include the derivation of kinetic type equations from particle and plasma systems, state-of-the-art numerical methods, studies of multiscale phenomena, and the applications of kinetic equations in physics, chemistry, computer sciences appearing in  life sciences, social sciences, and machine learning. This workshop will offer an exciting opportunity to connect researchers from all stages and sub-areas and spark new ideas.

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.

Tribute to Hamilton's graffiti of the Quaternion Division Algebra, County Dublin, Ireland. Photo: Professor Peter Gallagher, Director Dublin Institute for Advanced Studies Dunsink Observatory (courtesy DIAS)

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.

This workshop features a series of invited talks by experts across the fields of low-dimensional topology, homogeneous dynamics, and the geometry of symmetric spaces. Spanning all career stages, the event aims to foster a collaborative and supportive environment, particularly for early-career mathematicians, encouraging engagement, learning, and exploration in a welcoming academic setting.

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.

Image by Elliot Kienzle

This workshop will bring together theoretical physicists, representation theorists, algebraic geometers and symplectic geometers interested the connections between quantum field theory and geometric representation theory. The main topics to be discussed are mathematical aspects of 2d, 3d and 4d supersymmetric field theories, such as: topological twists and the resulting Higgs and Coulomb branches, relations to quantization and categorification, representations of vertex operator algebras, connections to enumerative geometry and quantum K-theory and elliptic cohomology, relations to knot homology and, finally, connections to the (relative) geometric Langlands program.