SEMINAR: Groups and Combinatorics Seminar: The Cayley Isomorphism (CI) problem


Groups and Combinatorics Seminar: The Cayley Isomorphism (CI) problem 
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Groups and Combinatorics Seminar
Joy Morris (University of Lethbridge, Canada)
will speak on
The Cayley Isomorphism (CI) problem
at 12 noon in MLR2 on Tuesday 8th of March
Abstract: In a perfect world in which all isomorphisms between graphs must be in
some sense ``natural," it would be possible to attack the problem of
determining whether or not given graphs are isomorphic, simply by
checking a (hopefully small) class of ``natural" isomorphisms. For
Cayley graphs, ``natural" isomorphisms between the graphs Cay(G;S)
and Cay(G;S') on the group G, would consist exclusively of automorphisms of the group G. Alas, our world is not perfect. However, there are some Cayley graphs
X=Cay(G;S) for which the isomorphism problem can be solved in this manner. That is, for such a graph X, the Cayley graph Cay(G;S') is isomorphic to X if and only if there is an automorphism of G that takes S to S' (and hence acts as a graph isomorphism). Such a graph is said to have the Cayley Isomorphism, or CI, property.
Furthermore, there are some groups G for which every Cayley graph Cay(G;S) has the CI property; these groups are said to have the CI property. The Cayley Isomorphism problem is the problem of determining which graphs, and which groups, have the CI property.
In this talk, I will discuss the motivation and background of the CI
problem (which stems from a 1977 paper by Laszlo Babai), and survey
some of the results that have been obtained on this problem.
Traditionally, the problem has been confined to finite Cayley graphs.
Towards the end of the talk, I will discuss the extension of this
problem to infinite graphs, and some results I have obtained on
locally finite graphs in joint work with Babai.
All welcome
Speaker(s) 
Joy Morris

Location 
Maths Lecture Room 2


Contact 
Michael Giudici
<[email protected]>

Start 
Tue, 08 Mar 2011 12:00

End 
Tue, 08 Mar 2011 12:45

Submitted by 
Michael Giudici <[email protected]>

Last Updated 
Thu, 03 Mar 2011 09:42

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