Matroid Week at CRM: A Collaborative Dive into Combinatorial Geometries

From October 13 to 17, 2025, the CRM hosted Matroid Week, a research school on combinatorial geometries and matroid theory. Courses by Laura Anderson and Geoff Whittle explored intersection properties and structural emergence in matroids. The event fostered deep theoretical exchange, international collaboration, and a vibrant research community.

The school featured two main courses led by prominent figures in the field:

Laura Anderson, professor at Binghamton University, focuses her research on the interplay between combinatorics and topology, especially oriented matroids, convex polytopes, and combinatorial models of topological spaces. She is the author of Oriented Matroids (Cambridge University Press, 2025), a geometrically motivated and accessible introduction to the subject. In her course, Intersection properties in oriented matroids, Anderson explored how non-realizable matroids can violate basic geometric and topological intuitions. She discussed properties such as the Euclidean property and other intersection phenomena that challenge our understanding of combinatorial space.

Geoff Whittle, professor at Victoria University of Wellington, is known for his contributions to the structural theory of matroids. In his course, The impossibility of chaos: how structure arises in matroid theory, Whittle showed how, despite the apparent wildness of general matroids, structure inevitably emerges. He explained how the exclusion of certain substructures leads to highly organized classes of matroids, such as binary matroids and those representable over all fields, drawing on seminal theorems by Tutte and Seymour.

In addition to the courses, the week included collaborative working sessions and open discussions around problems proposed by the speakers. These activities will continue in the coming weeks as part of the Intensive Research Programme, which features specialized seminars and will culminate in a closing conference in November.

Matroid Week was a vivid example of how mathematical research can combine theoretical depth, international collaboration, and a strong sense of community. At CRM, we celebrate the success of this initiative and look forward to the new research directions it will inspire.