Charlotte Scott Centre for Algebra

School of Mathematics & Physics, University of Lincoln

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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One comment on “Algebra Seminar by Nick Gill

  1. Evgeny Khukhro
    November 25, 2018

    Reblogged this on Maths & Physics News.

    Like

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This entry was posted on November 21, 2018 by in research, Seminar, Visitors.
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