Category Archives: exposition

a post aimed to teach something

The Sylvester design

The Sylvester graph There is a distance-transitive graph on 36 vertices with valency 5 known as the Sylvester graph. The graph was first constructed by Norman Biggs and his co-authors in their work on small distance-transitive graphs. I asked Norman … Continue reading

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Synchronization and separation in the Johnson schemes

Today a paper by Mohammed Aljohani, John Bamberg and me went on the arXiv on this topic. Here is a brief summary of what it is about. Synchronization comes in several flavours, and the point of the paper is to … Continue reading

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Notes on Counting

My book Notes on Counting: An Introduction to Enumerative Combinatorics should be published by Cambridge University Press in June this year, as part of the Australian Mathematical Society Lecture Series. If you have read some of my lecture notes on … Continue reading

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Power graphs of torsion-free groups

Today a paper on this topic appeared on the arXiv. I will say a bit about its contents, and how it came about. The power graph of a group G has vertex set G, with an edge from x to … Continue reading

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Multifractal analysis

Yesterday, the Edinburgh Mathematical Society met in St Andrews. Thomas Jordan gave a talk on multifractal analysis. I had no idea what this was, and went along without too much expectation of being enlightened. But Thomas began with a well-chosen … Continue reading

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Sum-free sets

This semester, Han Yu has run a reading group on Arithmetic Combinatorics. Mostly we have been following the excellent notes by Tuomas Orponen. I gave two talks. The first was a proof of the result of Ellenberg and Gijswijt on … Continue reading

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The march of truth

You can find a thing I wrote about this on the Institute of Art and Ideas website at https://iainews.iai.tv/articles/the-march-of-truth-auid-788, as part of a “conversation” on The Limits of Reason.

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