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# Category Archives: exposition

## Primitive switching classes

Last year I wrote here about switching classes of graphs for which the switching class has a primitive automorphism group. (I repeat the definitions briefly below.) I conjectured that, except for the trivial switching classes of the complete and null … Continue reading

Posted in exposition, mathematics
Tagged Akos Seress, Don Taylor, Pablo Spiga, primitive group, switching class, two-graph
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## Automorphism groups of hypergraphs

I am getting old and forgetful, but I don’t think I said anything here about this problem yet. If I did, apologies for the repetition – but there is something new to report! In April, Laci Babai and I finally … Continue reading

Posted in exposition, mathematics
Tagged Akos Seress, hypergraphs, Laci Babai, Pablo Spiga, primitive groups
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## Busy times, 9: Beyond the limit in St Petersburg

Anatoly Vershik is a universal mathematician, with influential work in asymptotic combinatorics, groups and group actions, probability, mathematical physics, and many other areas. This week, I was in St Petersburg for a conference with the wonderful title “Representations, Dynamics, Combinatorics: … Continue reading

Posted in events, exposition, mathematics
Tagged Anatoly Vershik, asymptotic combinatorics, Ramsey theory, St Petersburg, string theory
5 Comments

## Categorification, step 1

Today at the St Petersburg meeting, Igor Frenkel talked about categorification. He explained that there are five levels (maybe more!) and one has to take certain steps between them; he illustrated with an example, where level 0 was Jacobi’s Triple … Continue reading

## Terminology: association scheme or coherent configuration?

At the Villanova conference, many of the talks were about association schemes or coherent configurations, or indeed generalisations of these. A certain tension between different uses of these terms was evident. I’d like to set down my own views here. … Continue reading

Posted in exposition, history
Tagged association scheme, Bose, coherent configuration, Higman, Leman, Mesner, Nair, Schur ring, Shimamoto, Terwilliger, Weisfeiler
2 Comments

## Futoshiki squares

Futoshiki is a puzzle in the spirit of sudoku, involving constructing a Latin square from some partial information, which can be found in some newspapers now, including the Saturday Guardian. Probably someone has looked at the mathematics of futoshiki, but … Continue reading

## Busy times, 2

Some progress since the last report: the marking is nearly finished! This is just as well, since they have spent the morning drilling in the courtyard and I can’t stand a lot more of it. At first it was rather … Continue reading

## Overload

Today is a bank holiday (even here in Scotland). I am sitting at home working. I have fallen so far behind that there is no alternative. Part of the trouble is that, over the next few months, I am giving … Continue reading

Posted in events, exposition
Tagged infinity, paradox, synchronization, the party problem, the random graph, triangle-free graphs, two-graphs
2 Comments

## How the light gets in, 2014

Last year, I went to the festival How the Light Gets In in Hay-on-Wye, where I took part in a couple of panel discussions. It was a lovely day out, which I described here. At this year’s festival in late … Continue reading

Posted in events, exposition, history
Tagged Goedel's theorem, Hay-on-Wye, infinity, Institute of Arts and Ideas, music, paradox, philosophy
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## Notes on moonshine

A recent conversation reminded me that I had a set of notes on a talk I gave, based on an extended talk by V. Nikulin to the London Algebra Colloquium, about Borcherds’ proof of the moonshine conjecture (for which he … Continue reading