SEMINAR: Groups and Combinatorics Seminar: The Weiss Conjecture and inspirations thereof


Groups and Combinatorics Seminar: The Weiss Conjecture and inspirations thereof 
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Time and place: 16:00 Friday 20 May in Weatherburn LT
Speaker: Luke Morgan (UWA)
Title: The Weiss Conjecture and inspirations thereof
Abstract: In 1979 Richard Weiss made a beautiful conjecture: There exists a function f on the natural numbers such that, for each Gvertextransitive locallyprimitive graph X, the order of a vertexstabiliser is bounded by f(d), with d the valency X. Although the conjecture remains open in full generality, many mathematicians have been attracted to work on this problem, and in several interesting cases it has been shown that the conjecture is true. As well as proofs of (cases of) the statement, Richard’s conjecture also spurred people to understand vertextransitive graphs with local actions of certain flavours, such as locallyquasiprimitive graphs. This lead to the Praeger Conjecture of 2000, and for locallysemiprimitive graphs, the PotocnikSpigaVerret Conjecture of 2012. At this point the graphs faded to the background and general questions about semiprimitive permutation groups were raised. These turned out to be quite difficult, but one can say something. I’ll give an overview of some of these recent results and describe what we know on the various conjectures  that is  an overview of the wonderful mathematics that was inspired by Richard’s Conjecture.
Contact 
Tomasz Popiel
<[email protected]>

Start 
Fri, 20 May 2016 16:05

End 
Fri, 20 May 2016 17:05

Submitted by 
Tomasz Popiel <[email protected]>

Last Updated 
Tue, 17 May 2016 10:31

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