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CATEGORIES:Combinatorics Seminar
SUMMARY:Well-quasi-ordering binary matroids (Aitken Lectur
e) - Geoff Whittle (Victoria University of Welling
ton)
DTSTART;TZID=Europe/London:20111013T143000
DTEND;TZID=Europe/London:20111013T153000
UID:TALK32142AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32142
DESCRIPTION:The Graph Minors Project of Robertson and Seymour
is one of the highlights of twentieth-century math
ematics. In a long series of mostly difficult pape
rs they prove theorems that give profound insight
into the qualitative structure\nof members of prop
er minor-closed classes of graphs. \nThis insight
enables them to prove some remarkable banner theor
ems\, one of which is that in any infinite set of
graphs there is one that is a minor of the other\;
in other words\, graphs are well-quasi-ordered un
der the minor order.\n\nA canonical way to obtain
a matroid is from a set of columns of a matrix ove
r a field. If each column has at most two nonzero
entries there is an obvious graph associated with
the matroid\; thus it is not hard to see that mat
roids generalise graphs. Robertson and Seymour alw
ays believed that their results were special cases
of more general theorems for matroids obtained fr
om matrices over finite fields. For over a decade
\, Jim Geelen\, Bert Gerards and I have been worki
ng towards achieving this generalisation. In this
talk I will discuss our success in achieving the g
eneralisation for binary matroids\, that is\, for
matroids that can be obtained from matrices over t
he 2-element field.\n\nIn this talk I will give a
very general overview of my work with Geelen and
Gerards. I will not assume familiarity with matroi
ds nor will I assume familiarity with the results
of the Graph Minors Project.
LOCATION:MR12
CONTACT:Andrew Thomason
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