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.

The workshop will bring together researchers at the forefront of ongoing work in motivic homotopy theory.  Topics will include the application of motivic techniques to: geometry of affine algebraic varieties and algebraic vector bundles; computations in classical algebraic topology such as homotopy groups of spheres; and enumerative geometry.  The workshop will also consider the internal foundational development of motivic homotopy theory itself.

This workshop presents introductory talks and new trends in tropical geometry and algebraic combinatorics, including interactions between tropical geometry and enumerative, logarithmic, nonarchimedean, and real algebraic geometry, mirror symmetry and symplectic geometry, moduli spaces in tropical geometry, the geometry of matroids, integrable systems and dynamical combinatorics, combinatorial representation theory, geometry of polynomials, combinatorial varieties and connections to symmetric function theory and cluster algebras.