This week I am at the 23rd British Combinatorial Conference in Exeter. I haven’t been to one for 6 years so it has been good catching up with people who I haven’t seen for a long time, and meeting others for the first time, including some new academic brothers and sisters. It is also my third conference in a row which has meant three weeks worth of cooked breakfasts.

Two highlights from the plenaries so far have been Ian Wanless’s talk on transversals in Latin squares and Bruce Sagan’s on the cyclic sieving phenomenon. During Vladimir Nikiforov’s plenary talk we all had to evacuate the building. The rumour is that someone pressed the wrong button.

There were also four parallel sessions of contributed talks which means a bit of jumping around going to different rooms. I went to many good talks. Some particularly interesting ones were:

- Simon Blackburn’s on the probability that two elements in a group are conjugate;
- Bill Martin’s on cometric association schemes having irrational eigenvalues;
- Jonas Hagglund’s on the cycle double cover conjecture and the hunting of the snark. He had enumerated all small snarks and amongst them found counterexamples to many conjectures about cycle decompositions (but not the cycle double cover conjecture itself);
- Andrej Kisielwicz’ talk on totally symmetric coloured graphs;
- David Penman’s talk on the roots of the fixed point polynomal of a permutation group.

I spoke about the work with John, Gordon, Joy Morris and Pablo Spiga on groups acting point-primitively and line-primitively on a generalised quadrangle. The slides are here and we should be uploading the paper to the arxiv soon.

This is the last of the conferences as part of this trip but I am off to the University of Southampton next week to visit Tim Burness so the cooked breakfasts may continue.

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