Seminar series
Date
Tue, 18 Oct 2011
Time
16:00 -
17:00
Location
L1
Speaker
Professor Geoff Whittle
Organisation
Victoria University of Wellington
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.