# Algebra Seminar by Nick Gill

On Wednesday the 28th of November 2018, Nick Gill (University of South Wales) will be visiting the Charlotte Scott Centre for Algebra and giving a seminar on Cherlin’s conjecture for finite binary permutation groups. His talk will be at 4.30pm in INB 3305, and the abstract for his talk is as follows:

Abstract:

A mathematical object C is called HOMOGENEOUS if any local symmetry can be extended to a symmetry of C itself. The category of vector spaces, for instance, is replete with homogeneous objects: if U_1 and U_2 are vector subspaces of V that are symmetric, i.e. there is an invertible linear transformation T between them, then we know that we can extend T to an invertible linear transformation V -> V.

In other categories, though, homogeneous objects are hard to find — for instance, if one considers the category of graphs, a classical theorem of Sheehan/ Gardiner tells us that there are only a couple of infinite families, plus a couple of sporadic examples. Our interest lies in understanding Gardiner’s theorem as a special case of a general theory concerning HOMOGENEOUS RELATIONAL STRUCTURES. This wider perspective allows us to (a) generalize Gardiner’s result; (b) understand the presence of sporadic examples in Gardiner’s result; (c) understand relational homogeneity for any finite permutation group.

This is joint work with Francesca Dalla Volta, Francis Hunt, Martin Liebeck and Pablo Spiga.

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