# Discovering Mathematical Tourism

Sometimes you don’t have to go far to find travel inspiration and a change of scenery. In my search of the world for sites of mathematical significance, it turned out I’d been overlooking one practically on my doorstep! The Union Canal, near Falkirk In 1822 the Union Canal opened, providing (with the Forth and Clyde …

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# The Diverse Faces of Arithmetic- Notes on Sequences

View as: At The Diverse Faces of Arithmetic there were a pair of (early morning!) overview lectures for postgraduates. I’ve finally got around to typesetting my notes from the first, Tom Ward’s session on recurrence sequences, available as pdf via the above link. The topics included are divisibilty sequences and primitive divisors; linear recurrences; elliptic …

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# The Diverse Faces of Arithmetic

I shall be attending “The Diverse Faces of Arithmetic” in Norwich next week; taking a break from cyclotomic thoughts to revisit some topics I’ve mentioned here in the past, such as elliptic divisibility sequences.

# Young Researchers in Mathematics

There are now some videos available from the Beyond Part III / Young Researchers in Mathematics conference I attended earlier this year. Of particular note is David Spiegelhalter’s plenary lecture on probability and uncertainty. I summarised one of the ideas from that talk – the micromort – on Everything2, mentioning a comparison between the risks …

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# Workshop on Discovery and Experimentation in Number Theory

I’m back from the Fields Institute in Toronto, where I spoke at the above workshop, on my usual topic of cyclotomic and 4-cyclotomic matrices/graphs. During the talk I described my conjecture that a graph is maximal cyclotomic if-and-only if it’s 4-cyclotomic, and after an hour at the blackboards with James McKee I now have a …

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# Geometry Club Talk: Why Cryptography Doesn’t Guarantee Security

Tomorrow, in what seems to be becoming an annual tradition, I’ll be giving a talk on cryptography at the Geometry Club. Since it’ll be a talk-and-chalk style seminar, I don’t have any slides to make available, but many of the topics I’ll be discussing have appeared earlier on this blog or everything2. In particular, I’m …

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# An infinite family of n-hypercubes

Having hit a bit of a wall trying to prove that a maximal cyclotomic matrix necessarily squares to 4I, I’ve been exploring related questions instead. For instance, it only took a couple of tweaks to my code to search for matrices that square to 3I instead of 4I; there turn out to be only finitely …

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# A dangerous assumption

I’ve often said that trying to explain your work to others is the best way to check you understand it, and whilst preparing for this week’s talk at Cambridge (which was apparently well received!) I started to have some doubts about an algorithm I’d been using. In the end I didn’t go into enough technical …

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