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# Category Archives: exposition

## Wiles and Langlands

One of the best things that pops regularly into my pigeonhole is the European Mathematical Society Newsletter. The current issue, number 104, is particularly rich in interesting articles. For example, there is the transcript of a talk by Christian Krattenthaler … Continue reading

Posted in exposition, mathematics and ..., Uncategorized
Tagged Diophantine equations, Galois representations, Langlands, Wiles
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## Infinity and Foundation

After the reviving effect of a week’s holiday, I have been thinking about Zermelo–Fraenkel set theory, inspired by a very nice student project I supervised (about which I hope to say something here sometime soonish). I have come across a … Continue reading

## 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

## 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

Posted in exposition, Uncategorized
Tagged association scheme, Peter Keevash, Philippe Delsarte, separation, synchronization
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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

## 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

Posted in exposition
Tagged power graph, summer research project, torsion-free group
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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

Posted in exposition
Tagged Besicovich, Edinburgh Mathematical Society, Hausdorff dimension
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