<p>Calabi–Yau manifold. (Image attribution: Lunch on Wikipedia)</p>

This workshop is on recent developments in representation theory, quantum field theory, and motivic homotopy theory. Contemporary representation theory has been increasingly influenced by the mathematical development of supersymmetric gauge theories and mirror symmetry. Motivic homotopy theory—a version of homotopy theory for algebraic varieties and solutions to polynomial equations—has seen widespread modern applications. This three-day workshop aims to introduce researchers to these fields and their open problems, and to highlight recent progress. The workshop will include research lectures as well as activities to promote interaction and connections between the participants. This workshop is open to all mathematicians.

Under the light of suspended spheres, the QFT wizard dangles groups and their duals over a boiling cauldron of motives. (Drawn by Rok Gregoric)

The goal of this introductory workshop is to showcase some of the recent developments in motives and quantum field theory, with a focus on giving a high-level, but "outsider-friendly" introduction to both subjects. It will feature lectures introducing the modern formalism of sheaf theories, supersymmetric gauge theories, geometric representation theory and motivic spectra.

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.

The Simons Laufer Mathematical Sciences Institute (SLMath) will host the 2026 Modern Math Workshop (MMW) as part of the SACNAS Annual Conference. The Modern Math Workshop encourages undergraduates to pursue careers in the mathematical sciences, and builds research and networking opportunities among undergraduates, graduate students and recent PhDs in the mathematical sciences.

A contour used in [Calegari–Dimitrov–Tang, 2024] to prove L(2, χ−3) ∈/ Q.

In 1978, Apéry proved that ζ(3) was irrational. Almost 50 years later, we still don’t know if ζ(5) is irrational. Why not? The goal of this workshop is to bring together experts on explicit rational approximations and motivic differential equations to consider new approaches to these questions.

The perfectoid infinite level modular curve

This workshop will focus on geometric Sen theory, its connections to the p-adic Simpson correspondence, and applications to modularity. In addition to three mini-courses, the workshop will feature research talks on related recent developments in p-adic Hodge theory and p-adic geometry.  

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.

Fano plane

The workshop will include three minicourses on key topics in Algebraic Combinatorics & Tropical Geometry: combinatorial representation theory, combinatorial algebraic varieties and their connections to various polynomial bases, combinatorial and algebro-geometric facets of matroids, enumerative tropical geometry, real aspects of tropical geometry and connections with A1-homotopy theory.
The minicourses will be intended for a broad audience, with the goal of providing background and motivation in these topics.

<p>This figure encodes the combinatorics of a triangulation of the permutahedron.&nbsp;&nbsp;Figure appears in Defant--Sherman-Bennett--<wbr />Williams&nbsp;<a data-saferedirecturl="https://www.google.com/url?q=https://arxiv.org/pdf/2509.11497&amp;source=gmail&amp;ust=1769544428157000&amp;usg=AOvVaw1E-v0MZ1v_EyqlWLiqlPNw" href="https://arxiv.org/pdf/2509.11497" target="_blank">https://arxiv.org/<wbr />pdf/2509.11497</a>.</p>

This workshop will bring together researchers at the cutting edge of algebraic combinatorics.   The topics will include integrable systems, dynamical combinatorics, combinatorial representation theory with connections to theoretical computer science, the geometry of polynomials, cluster algebras, combinatorial algebraic geometry, and symmetric functions.  

The discriminant locus in the base of a Lagrangian torus fibration on the quintic threefold.

This workshop will focus on enumerative aspects of tropical geometry and tropical moduli spaces. The meeting will bring together researchers from several different areas in real and complex geometry, symplectic geometry, mirror symmetry and non-Archimedean geometry.