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# Category Archives: exposition

## Pappus and Diophantus

This post is inspired by a nice article by Adrian Rice and Ezra Brown in the latest BSHM Bulletin, titled “Commutativity and collinearity: a historical case study of the interconnection of mathematical ideas, Part II”. Pappus’ Theorem states that, if … Continue reading

Posted in exposition, history
Tagged Fano plane, Kirkman, Pappus' Theorem, Steiner triple system, two squares equality
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## Conventions

I woke this morning thinking about something I learned in physics at school. A wire carrying a current in a magnetic field is acted on by a force (if it is not parallel to the field): in what direction does … Continue reading

## There is no McLaughlin geometry

Congratulations to Patric Östergård and Leonard Soicher, who have just completed a big computation whose conclusion is “There is no McLaughlin geometry”. The run-time of the computation was about 250 core-years. So what did they compute, and why does it … Continue reading

## Private information retrieval

Yesterday I was at a meeting on this subject at Royal Holloway, organised by Simon Blackburn. The subject is relatively young; it began in 1995 with a paper by Chor, Goldreich, Kushilevitz and Sudan. At the meeting, Alex Vardy gave … Continue reading

## An LTCC book

The Taught Course Centres for PhD students in the Mathematical Sciences were set up as the result of a recommendation of the last-but-one International Review of Mathematics. The review panel said that the highly specialised nature of British PhDs meant … Continue reading

## The Higman–Thompson groups

I celebrated the last day of spring last week with the appearance of two substantial papers on the arXiv: one with Maria Elisa Fernandes, Dimitri Leemans, and Mark Mixer, proving that the maximum rank of a regular polytope whose group … Continue reading

Posted in exposition
Tagged automata, Cantor space, Grtaham Higman, homeomorphisms, regular polytopes, Richard Thompson, synchronization, transducers
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## Permutation groups in Bristol

On 1 June, a meeting of the “Groups and Applications” triangle was held in Bristol. (This peripatetic meeting was a long thin triangle with vertices London, Birmingham and Manchester, but with the inclusion of Bristol it is not clear what … Continue reading