This research school is part of the
MDM FOCUSED RESEARCH PROGRAMME ON COMBINATORIAL GEOMETRIES & GEOMETRIC COMBINATORICS
Research school on Combinatorial Geometries and Geometric Combinatorics - Matroid week
Sign into October 17, 2025
Venue: Centre de Recerca Matemàtica
Room: Auditorium
EVENT SUMMARY
description
The research school will consist of 4 advanced courses.
Intersection properties in oriented matroids
Laura Anderson
Binghamton University
Abstract: Consider a rank 2 set S and a rank 3 set T of vectors in a real vector space such that the rank of their union is less than 5. Then of course there is a nonzero vector that is in the intersection of the spans of S and T: this is the sort of intersection property we use all the time in convex geometry. In contrast, given a (non-realizable) oriented matroid M and sets S and T of elements satisfying the same rank conditions, it may be impossible to add a nonzero element to M that’s in the span of both S and T.
It turns out that the oriented matroids that lack intersection properties also violate our intuition in a lot of other ways, both geometrical and topological. Indeed, they seem to offer the best answers to the global question: How weird can non-realizable oriented matroids get? Their existence has been known since nearly the dawn of oriented matroids, but many basic questions about them remain open.
By far the most widely studied intersection property is the Euclidean Property, about sets of rank 2 and r-1 in a rank r oriented matroid. We’ll discuss what’s known about it in some depth, then venture into the less-understood realm of broader intersection properties.
The impossibility of chaos: how structure arises in matroid theory
Geoff Whittle
Victoria University of Wellington
Abstract: In full generality matroids are famously wild. Yet we are rapidly forced into tame subclasses. Tutte proved that it suffices to exclude the 4-point line as a substructure to guarantee that a matroid to belong to the highly structured class of binary matroids. On the other hand, Seymour famously proved that a matroid is representable over all fields if and only if it can be built, in a tree-like way, from graphic matroids, the duals of graphic matroids and a single exceptional matroid. These theorems have been seminal and have led to what is now a well developed area of research. My goal will be to give insight into this world as well as some of its key proof techniques.
Organising Committee
Kolja Knauer | Universitat de Barcelona – Centre de Recerca Matemàtica
Anna de Mier | Universitat Politècnica de Catalunya
Arnau Padrol | Universitat de Barcelona – Centre de Recerca Matemàtica
Julian Pfeifle | Universitat Politècnica de Catalunya
Vincent Pilaud | Universitat de Barcelona – Centre de Recerca Matemàtica
Scientific Committee
Martina Juhnke | Universität Osnabrück
Peter Nelson | University of Waterloo
Felipe Rincón | Queen Mary University of London
Martha Yip | University of Kentucky
schedule
Monday October 13th | Tuesday October 14th | Wednesday October 15th | Thursday October 16th | Friday October 17th | |
9:30 – 9:50 | Registration | ||||
9:50 – 10:00 | Welcome | ||||
10:00 – 11:00 | Course 1 Intersection properties in oriented matroids Laura Anderson Binghamton University | Course 1 Intersection properties in oriented matroids Laura Anderson Binghamton University | Course 1 Intersection properties in oriented matroids Laura Anderson Binghamton University | Course 2 The impossibility of chaos: how structure arises in matroid theory Geoff Whittle Victoria University of Wellington | Course 2 The impossibility of chaos: how structure arises in matroid theory Geoff Whittle Victoria University of Wellington |
11:00 – 11:30 | Coffee break | Group picture + coffee break | Coffee break | ||
11:30 – 13:00 | Exercise session | Exercise session | Exercise session | Exercise session | Exercise session |
13:00 – 14:30 | Lunch | ||||
14:30 – 15:30 | Course 2 The impossibility of chaos: how structure arises in matroid theory Geoff Whittle Victoria University of Wellington | Course 2 The impossibility of chaos: how structure arises in matroid theory Geoff Whittle Victoria University of Wellington | Course 1 Intersection properties in oriented matroids Laura Anderson Binghamton University | Presentation of research projects | |
15:30 – 15:45 | Break | Break | |||
15:45 – 17:15 | Exercise session | Exercise session | Exercise session | ||
20:00 | Social dinner | ||||
LIST OF PARTICIPANTS
| Name | Institution |
|---|---|
| Vincent Pilaud | Universitat de Barcelona |
| Arnau Padrol Sureda | Universitat de Barcelona |
| Anouk Brose | University of California Davis |
| Leo Jiang | University of Toronto |
| William Dugan | Universitat de Barcelona |
| Yirong Yang | University of Washington - Seattle |
| Torben Donzelmann | University of Osnabrück |
| Jhon Bladimir Caicedo Portilla | University of Osnabrück |
| Teemu Lundström | Aalto University |
| Chiara Giardino | Ruhr University Bochum |
| Chenying Lin | University of Regensburg |
| Egor Bakaev | University of Copenhagen |
| Natasha Crepeau | University of Washington - Seattle |
| Félix Gélinas | York University |
| Leonardo Saud Maia Leite | Royal Institute of Technology |
| Marguerite Bin | University of Lorraine |
| Alexandros Leivaditis | Ruhr University Bochum |
| Laura Anderson | Binghamton University |
| Juliana Curtis | University of Washington - Seattle |
| Jan Stricker | Goethe University Frankfurt |
| David Alcántara | Universidad de Cantabria |
| Hung Hoang | Vienna University of Technology |
| Geoff Whittle | Victoria University of Wellington |
| Dmitry Mineev | Bar-Ilan University |
| Hoi Ping Luk | Západoceská univerzita v Plzni |
| Niraj Velankar | University of Greifswald |
| Sania Asif | Henan Academy of Sciences |
| Bilal Khan | Henan Academy of Sciences |
| Spencer Backman | University of Vermont |
| Baptiste Gros | University of Montpellier |
| Jette Gutzeit | University of Zurich |
| Lauren Nowak | University of Washington - Seattle |
| Anna de Mier | Universitat Politècnica de Catalunya |
| Zia Ullah Khan | Shanghai University of Electric Power |
| Danai Deligeorgaki | Universitat de Barcelona |
| Ileana Gonzalez Escalante | Universidad Nacional Autonoma de Mexico |
| Florian Rieg | Goethe University Frankfurt |
| Chiara Meroni | ETH Institute for Theoretical Studies |
| Raman Sanyal | Goethe University Frankfurt |
| Sophia Keip | FernUniversität in Hagen |
| Kolja Knauer | Universitat de Barcelona – Centre de Recerca Matemàtica |
| Federico Lazzeri | Royal Institute of Technology |
| Julian Pfeifle | Universitat Politècnica de Catalunya |
| Francisco Santos Leal | Universidad de Cantabria |
| Pallavi Panda | University of Paris 13 |
| Richard Danner | University of Vermont |
| Elna Guardiola | Universitat de Barcelona |
| Júlia Sabiote Cartes | Universitat de Barcelona |
| Miquel Ortega | Universitat Politècnica de Catalunya |
INVOICE/PAYMENT INFORMATION
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Acknowledgements
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