Information Technology seminars
Is the missing axiom of matroid theory lost forever?
- Date and time:
- 20/02/2009, 11:00
- Location:
- Building: 63, Room: 115, Clayton Campus
- Presenters:
- Prof Geoff Whittle (Victoria University of Wellington)
- Abstract:
- Matroids were introduced by Whitney in the 1930's to abstract the combinatorial properties of a finite set of vectors in a vector space. It seems clear that he had vector spaces over the reals in mind. But it turns out that many structures arise that satisfy the axioms of a matroid that are not isomorphic to ones obtained from vectors over the reals. The question, posed by Whitney himself, arises whether extra axioms can be added to the axioms of matroids to characterise matroids over the reals. While this is not really a well-posed question the general belief in the community arose that the answer is negative as there is a paper in the literature entitled "The missing axiom of matroid theory is lost forever". But a careful reading of the paper shows that the situation is far more complicated and Whitney's question is still unresolved. In this talk I will discuss this issue. No knowledge of matroid theory will be assumed. While the talk is about matroids the theme is more general. It is, in some sense, a moral tale.
- Speaker biographies:
- Geoff Whittle was born in Tasmania where he went to university and (eventually) gained a PhD in 1984. Since 1992 he has been at Victoria University of Wellington in New Zealand where he is currently a Professor of Maths. Instead of normal research interests he has an unhealthy obsession with long standing problems in matroid representation theory. On good days he fantasizes that he will live long enough to see some of them solved.
- Enquiries:
- Graham Farr
