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Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Cluster algebras, webs and canonical bases are three different methods that mathematicians have developed in order the understand the symmetries of certain mathematical structures. Each of these three ways arose from, and has applications to, different areas of mathematics. These areas include algebraic geometry, representation theory, topology, and combinatorics, as well as physics. The goal of this workshop is to bring together experts and up-and-coming researchers from each of these areas in order to better understand the still mysterious connections between cluster algebras, webs, and canonical bases. A better understanding of these connections could allow for ideas from one area to be applied to solve problems in other areas.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Core objects of study in algebraic geometry and in commutative algebra are called varieties and rings, respectively. Varieties are geometric objects that consist of sets of solutions to polynomial equations. Each variety has a corresponding ring consisting of the polynomial functions that are defined on the variety.

Graph Theory and Combinatorics,    Geometry and Topology

The Fields Institute

This conference will honour the work of John F. (Rick) Jardine, a professor at the University of Western Ontario. Over his 40+ year career, Rick has made foundational contributions to homotopy theory, K-theory, and topological data analysis, in particular shaping the current landscape of homotopical algebra.

University of Ottawa

MMRT 2026 focuses on modern categorical and diagrammatic methods in representation theory, with particular emphasis on monoidal categories, categorification, and their applications to Lie algebras, quantum groups, and quantum symmetric pairs. The conference aims to bring together leading researchers and early-career mathematicians to exchange new techniques, highlight emerging connections with topology and quantum mathematics, and foster interaction across complementary modern approaches.

Quantum groups, quantum symmetric pairs, monoidal categories

Fields Institute, Toronto, Canada

Since its inception in 1981, the IWOTA has been at the forefront of fostering collaboration and advancing research in the field of operator theory and its diverse applications. Beginning as a modest gathering, IWOTA has evolved into a prestigious conference series, attracting leading mathematicians and engineers from around the globe. IWOTA has a rich history of conferences held in various countries, reflecting its global impact and reach. The diverse array of topics covered by IWOTA conferences underscores the interdisciplinary nature of operator theory and its applications. From differential equations to mathematical physics, IWOTA provides a platform for researchers to explore cutting-edge developments and collaborate on innovative solutions to complex problems.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Free noncommutative (nc) function theory is an analogue of classical function theory where one replaces functions between two complex vector spaces by functions between square matrices of all sizes over these vector spaces that respect matrix size, direct sums, and similarities. It has emerged in the last decade and a half as a vibrant research area with results that are sometimes similar to and sometimes strikingly different from the classical commutative setting, and with interconnections and applications ranging from free rings and free skew fields to free probability and random matrix theory to dimension independent linear matrix inequalities in systems and control. The purpose of this research in teams is to develop new relations between free probability and nc function theory by launching a systematic investigation and usage of asymptotic integration over classical compact matrix groups and their homogeneous spaces. We expect this to open the road for an asymptotic study of Hardy and Bergmann spaces of nc functions and exhibit completely new phenomena regarding Shilov boundaries and uniqueness sets in the nc setting.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

This workshop aims at bringing together an interdisciplinary scientific community to share some of the state-of-the-art results in the theory of Herglotz-Nevanlinna functions, and to solve common open problems lying at the frontier of pure mathematics, applied mathematics, physics, and engineering. Further development of this theory would lead to significant progress not only in the area of pure mathematics, but also in its applications to antennas, metamaterials, and composite materials.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Higher-rank graphs generalize path categories of directed graphs and are intricately connected to various mathematical disciplines. This workshop aims to illuminate the rich interplay between higher-rank graph C*-algebras and fields such as algebra, theoretical physics, and geometry. By examining how these algebras both influence and are influenced by these diverse areas, the event will provide insights into their broader implications and applications. The workshop will bring together experts from different fields and career stages, each offering a unique perspective on higher-rank graphs. and interactions.

Courses and Events for Math Students and Early Career Researchers,    Graph Theory and Combinatorics