Charlotte Scott Centre for Algebra

On Wednesday the 28th of November 2018, **Dr Nick Gill** (University of South Wales) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk “*Cherlin’s conjecture for finite binary permutation groups*”.

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…

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