Select Page

Matroid Week at CRM: A Collaborative Dive into Combinatorial Geometries

by | Oct 17, 2025 | CRM News

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.

From October 13 to 17, 2025, the Centre de Recerca Matemàtica (CRM) hosted the Research School on Combinatorial Geometries and Geometric Combinatorics – Matroid Week, an intensive school within the MdM research program. Over five days, researchers from around the world delved into matroid theory—a branch of combinatorics that connects deeply with geometry, algebra, and topology.

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.

Subscribe for more CRM News

Stay updated to our mailing list to get the lastest information about CRM activities.

Subscribe

CRM Comm

Natalia Vallina

CRMComm@crm.cat

 
László Lovász receives the 2025 Erasmus Medal in Barcelona

László Lovász receives the 2025 Erasmus Medal in Barcelona

by | Oct 17, 2025

Mathematician László Lovász received the 2025 Erasmus Medal from the Academia Europaea yesterday at the PRBB in Barcelona, where he delivered the lecture “The Beauty of Mathematics”. Renowned for his work in graph theory and discrete mathematics, Lovász has shaped...

Combinatorial Geometry Takes Shape at the CRM

Combinatorial Geometry Takes Shape at the CRM

by | Oct 14, 2025

For one week in early October, the Centre de Recerca Matemàtica became a meeting ground for the world of combinatorial geometry. The Polytope Week research school gathered more than fifty participants from three continents to study the interplay...