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SEMINAR: Mathematics & Statistics Colloquium

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Today's date is Thursday, February 25, 2021
Mathematics & Statistics Colloquium Other events...
Everyone is warmly invited to our Mathematics and Statistics Colloquium.

Talk title: The random graph and its friends

Talk abstract: There is a countably infinite graph R (first explicitly constructed by Richard Rado) with the following remarkable property: If we choose a countable random graph by selecting edges independently with probability 1/2, then with probability 1 it is isomorphic to R. (This fact was implicit in a paper of Erdos and Renyi at about the same time as Rado's construction.) The graph has many other surprising properties, and occurs in a number of guises.

It turns out that the graph is produced by a construction by Fraisse more than ten years earlier, which builds homogeneous relational structures with prescribed finite substructures, and shows its uniqueness. But even Fraisse had been anticipated by Urysohn, who showed (in a posthumous paper a quarter of a century earlier) that there is a unique homogeneous Polish space containing all finite metric spaces.

It is natural to ask what happens if we dualise Fraisse's construction by turning the arrows around. There is indeed a dual construction; among other things it gives a new way to build a remarkable topological space, the pseudo-arc.
Speaker(s) Professor Peter Cameron (University of St Andrews)
Location Blakers Lecture Theatre
Contact Luke Morgan <[email protected]>
URL https://www.maths.uwa.edu.au/research/colloquium
Start Thu, 15 Sep 2016 16:00
End Thu, 15 Sep 2016 17:00
Submitted by Luke Morgan <[email protected]>
Last Updated Mon, 12 Sep 2016 10:15
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