LMS Aitken Lecture: "Matroid Representation over Infinite Fields"
|
Tue, 18/10/2011 16:00 |
Professor Geoff Whittle (Victoria University of Wellington) |
Combinatorial Theory Seminar  |
L1 |
| A canonical way to obtain a matroid is from a finite set of vectors in a vector space over a field F. A matroid that can be obtained in such a way is said to be representable over F. It is clear that when Whitney first defined matroids he had matroids representable over the reals as his standard model, but for a variety of reasons most attention has focussed on matroids representable over finite fields. There is increasing evidence that the class of matroids representable over a fixed finite field is well behaved with strong general theorems holding. Essentially none of these theorems hold if F is infnite. Indeed matroids representable over the real– the natural matroids for our geometric intuition – turn out to be a mysterious class indeed. In the talk I will discuss this striking contrast in behaviour. | |||