Just a brief note that my second paper on my thesis topic has been accepted by the Journal of Number Theory. The full citation is: Graeme Taylor, Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields, Journal of Number Theory, Volume 132, Issue 4, April 2012, Pages 590-607, ISSN 0022-314X, [...]
Archive of posts filed under the Graph Theory category.
Cyclotomic Matrices and Graphs over the ring of integers of some imaginary quadratic fields
Online access to my first paper.
Cyclotomic Matrices and Graphs: Warwick
I’m continuing to tour my Cyclotomic Matrices and Graphs talk; today I presented it at the University of Warwick. Here’s the latest and greatest iteration of the slides, mostly unchanged except for the current state of the computer search for minimal noncyclotomics of at most ten vertices. I’d hoped to finish that this month, but [...]
Joint Mathematics Meetings 2011
I spent last week in New Orleans for the Joint Mathematics Meetings 2011. I’d made a rather last minute booking after noticing a couple of sessions could be useful, and hadn’t quite grasped the scale of the event. I’d normally think of 200 mathematicians as a large gathering, but the JMM had over six thousand [...]
Talks on Cyclotomic Matrices and Graphs
I’m speaking this afternoon at the Heilbronn Seminar in Bristol: my slides are available here. This is essentially (up to permutation, and modulo errors!) the talk I gave at Royal Holloway in October, although the last few slides have been replaced with a result I’ve found since then. I try to avoid technical details of [...]
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 [...]
What I’m working on…
Brief, fairly technical overview of what I’ve been working on these last few months.
Hard problems in graph theory
BICS Seminar by Keith Briggs.
Prospects in Mathematics (Durham 2005)
Summary of speakers and topics presented at a two-day pure mathematics conference for undergraduates.
