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Thompson groups

Nathan Barker - Thompson GroupsToday’s blackboard belongs to Nathan Barker at the University of Newcastle. Nathan works with Thompson groups, which were first studied in 1965 and provide examples of interesting phenomena in group theory.

Top-left is a realisation of the automorphism group of one of Thompson’s groups as a tree. On the right is a subgroup that may or may not have the property Nathan wants, and then Poincare’s disc model of the hyperbolic plane, and an annular strand diagram. The jumpy line drawing at the bottom is the Cayley graph of PSL(2,Z) – the group of all 2×2 integer-valued matrices with determinant 1, where matrices A and -A are considered to be the same.

The bottom-left section is some quantum computation stuff by somebody called Ben that nobody but him understands.

Thanks to Christian Perfect for taking and sending me this photo, and for providing details of what’s on the board.

Readers of this blog may also be interested in an article detailing the relationship between mathematicians and blackboards: http://www.sps.ed.ac.uk/__data/assets/file/0020/60518/Chalk.pdf

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