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 between geometry and combinatorics through lectures, exercises, and open discussions. Carolina Benedetti (Universidad de los Andes) and Raman Sanyal (Goethe-Universität Frankfurt) led the two main minicourses, introducing current advances on matroids, positroids, and moduli polytopes.
From October 6 to 10, the Centre de Recerca Matemàtica hosted the Research School on Combinatorial Geometries and Geometric Combinatorics – Polytope Week, a meeting point for researchers exploring the rich territory where geometry and combinatorics intersect. The activity was part of the MDM Focused Research Programme on Combinatorial Geometries and Geometric Combinatorics, coordinated by Kolja Knauer, Anna de Mier, Arnau Padrol, Julian Pfeifle, and Vincent Pilaud.
The activity showcased the growing dialogue between geometry and combinatorics, highlighting how shared methods and perspectives can drive advances across both fields.
More than fifty participants from universities across Europe, America, and Asia filled the CRM Auditorium for five days of lectures, problem sessions, and informal discussions. The schedule alternated between theoretical insights and hands-on work, creating a rhythm that blended the rigor of advanced training with the atmosphere of a collaborative workshop.
Carolina Benedetti (Universidad de los Andes) opened the week with her minicourse Perspectives on flags of matroids and positroids, introducing participants to a field that connects combinatorial structures with geometry and algebraic concepts from tropical mathematics. Through examples and open problems, Benedetti guided the audience toward questions still at the frontier of research, including subdivisions of polytopes linked to matroid theory.
In the second minicourse, Moduli polytopes: parametrizing combinatorial structures with polytopes, Raman Sanyal (Goethe-Universität Frankfurt) explored how complex discrete objects, such as permutations, rooted trees, or matroids, can be encoded as vertices of geometric shapes. His lectures revealed the capacity of this geometric viewpoint to understand, compare, and classify combinatorial structures.
Afternoons were devoted to exercise sessions and group work, giving participants the chance to test ideas and develop small collaborative projects. The week also included a session for research presentations and a social dinner that carried discussions well beyond the blackboard.
By the end of the school, what began as a deep dive into the geometry of polytopes had become a broader exchange of perspectives and techniques, linking students and researchers at different stages of their careers. The Polytope Week confirmed the dynamism of the community around combinatorial geometry.
Subscribe for more CRM News
Stay updated to our mailing list to get the lastest information about CRM activities.
|
|
CRM CommPau Varela
|
Mathematics and Machine Learning: Barcelona Workshop Brings Disciplines Together
Over 100 researchers gathered at the Centre de Recerca Matemàtica to explore the mathematical foundations needed to understand modern artificial intelligence. The three-day workshop brought together mathematicians working on PDEs, probability, dynamical systems, and...
Barcelona + didactics + CRM = CITAD 8
From 19 to 23 January 2026, the CRM hosted the 8th International Conference on the Anthropological Theory of the Didactic (CITAD 8), a leading international event in the field of didactics research that brought together researchers from different countries in...
Seeing Through Walls: María Ángeles García Ferrero at CRM
From October to November 2025, María Ángeles García Ferrero held the CRM Chair of Excellence, collaborating with Joaquim Ortega-Cerdà on concentration inequalities and teaching a BGSMath course on the topic. Her main research focuses on the Calderón problem,...
Fuel Cells, Filtration, and Decades of Collaboration: A Conversation with Brian Wetton
Brian Wetton, from the University of British Columbia, spent last October at CRM collaborating with Tim Myers on computational models for filtration systems. His career has evolved from pure numerical analysis to applied mathematics with industrial partners, working...
From Barcelona to West Bengal: Chemistry Meets Mathematics to Enhance Water Filter Design
Researchers at the Centre de Recerca Matemàtica, in collaboration with IIT Kharagpur and UPC, have developed a mathematical model that accurately predicts the performance of fluoride-removal water filters made of mineral-rich carbon (MRC) and...
Polytopes, Matroids, and the Friends You Make: Martina Juhnke on Two Months at the CRM
The Centre de Recerca Matemàtica recently hosted a research programme on Combinatorial Geometries and Geometric Combinatorics, focusing on the overlap between polytopes and matroids. Martina Juhnke, a member of the scientific committee, reflects on how this programme...
BAMB! 2025: Participants Return to the CRM for Research Stays
In October 2025, the Centre de Recerca Matemàtica hosted Josefine Meyer (ISTA) and Cate MacColl (University of Queensland) for a month-long research stay following their participation in the BAMB! Summer School. Despite studying vastly different subjects, from...
Connecting Shapes, Patterns, and Ideas: the Closing Conference on Combinatorial Geometries and Geometric Combinatorics
During five days, the CRM hosted the Closing Conference of the MDM Focused Research Programme on Combinatorial Geometries & Geometric Combinatorics. The event featured plenary talks, contributed sessions, and posters on topics from matroids and polytopes to...
Xavier Ros-Oton among the 65 most cited mathematicians in the world
ICREA professor at the Universitat de Barcelona and CRM affiliated researcher Xavier Ros-Oton appears on Clarivate's Highly Cited Researchers 2025 list, which this year reinstates the mathematics category after two years of exclusion.Citations are a strange way to...
New Horizons for H- and Γ-convergence: From Local to Nonlocal (and viceversa)
The researchers Maicol Caponi, Alessandro Carbotti, and Alberto Maione extended the H- and Γ-convergence theories to the setting of nonlocal linear operators and their corresponding energies. The authors were able to overcome the limitations of classical localization...
Diego Vidaurre joins the CRM through the ATRAE talent programme
Diego Vidaurre has joined the Centre de Recerca Matemàtica through the ATRAE programme, bringing his expertise in modelling spontaneous brain activity across multiple data modalities. His work focuses on understanding how the brain’s intrinsic dynamics shape...
El CRM a la Setmana de la Ciència: una ruta entre dones, formes i pensament
El CRM va participar en la 30a edició de la Setmana de la Ciència amb una ruta guiada que va combinar les biografies de dones matemàtiques amb obres d'art del centre, connectant ciència, història i creació artística.El 12 de novembre, el Centre de Recerca Matemàtica...