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Category Archives: exposition
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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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
Posted in exposition
Tagged Baire category, Calkin, density, Erdos, measure, Roth, Schoen, Schur, Szemeredi, van der Waerden
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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.
