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SUMMARY:Well-quasi-ordering binary matroids (Aitken Lecture) - Geoff Whitt
 le (Victoria University of Wellington)
DTSTART:20111013T133000Z
DTEND:20111013T143000Z
UID:TALK32142@talks.cam.ac.uk
CONTACT:Andrew Thomason
DESCRIPTION:The Graph Minors Project of Robertson and Seymour is one of th
 e highlights of twentieth-century mathematics. In a long series of mostly 
 difficult papers they prove theorems that give profound insight into the q
 ualitative structure\nof members of proper minor-closed classes of graphs.
  \nThis insight enables them to prove some remarkable banner theorems\, on
 e of which is that in any infinite set of graphs there is one that is a mi
 nor of the other\; in other words\, graphs are well-quasi-ordered under th
 e minor order.\n\nA canonical way to obtain a matroid is from a set of col
 umns of a matrix over a field. If each column has at most two nonzero ent
 ries there is an obvious graph associated with the matroid\; thus it is no
 t hard to see that matroids generalise graphs. Robertson and Seymour alway
 s believed that their results were special cases of more general theorems 
 for matroids obtained from matrices over finite fields. For over a decade
 \, Jim Geelen\, Bert Gerards and I have been working towards achieving thi
 s generalisation. In this talk I will discuss our success in achieving the
  generalisation for binary matroids\, that is\, for matroids that can be o
 btained from matrices over the 2-element field.\n\nIn this talk I will gi
 ve a very general overview of my work with Geelen and Gerards. I will not 
 assume familiarity with matroids nor will I assume familiarity with the re
 sults of the Graph Minors Project.
LOCATION:MR12
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