Thesis available
Downloadable copy of my thesis.
Archive of posts filed under the Postgrad category.
Content produced in relation to my studies at the University of Edinburgh.
Viva
Today I successfully defended my PhD thesis, Cyclotomic Matrices and Graphs. There are of course numerous corrections to be made, but I hope to have those done within the next couple of weeks and to make the final version available online. Until then, here is the abstract: We generalise the study of cyclotomic matrices – …
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 …
Continue reading ‘The Diverse Faces of Arithmetic- Notes on Sequences’ »
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 …
Continue reading ‘Workshop on Discovery and Experimentation in Number Theory’ »
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 …
Continue reading ‘Geometry Club Talk: Why Cryptography Doesn’t Guarantee Security’ »
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 …
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 …
MAGIC Talk
Slides for a talk on cyclotomic matrices/graphs given at the MAGIC conference in Manchester.
Colloquium Talk
Slides from a colloquium I gave on public key cryptography.
Geometry Club Talk: Computational aspects of ECDLP
Notes from my geometry club talk given April 18th, 2008.