I have now completed a series of introductory lectures on Graph Theory, for 3rd/4th year students at the University of Bristol. A set of written notes plus (less usefully) my slides are mirrored here. One student declared this to be “[the] most interesting course I have taken at Bristol Uni”, so take a look to …
Continue reading ‘‘Introduction to Graph Theory’ Lecture Materials’ »
Earlier this month I attended the 2013 Joint Mathematics Meetings, trading freezing Britain for sunny San Diego! This was the 119th annual meeting of the American Mathematical Society, the 96th of the Mathematical Association of America, my third trip to the US for a JMM, and the first at which I’ve given a talk. There …
I attended the 2013 Joint Mathematics Meetings in San Diego to present work at the AMS-SIAM Special Session on Mathematics of Computation: Algebra and Number Theory, II. Here are my slides, on Lehmer’s conjecture for Hermitian matrices over the Eisenstein and Gaussian integers.
In the next academic year I’ll be one of the lecturers for Topics in Discrete Mathematics at the University of Bristol. This comes in two flavours- the level H/6 unit MATH30002 for third-year students, and the level M/7 unit MATHM0009 for those in the fourth year (which adds a project component). This will be the …
I’m offering a couple of possible projects for third-year students at Bristol (i.e., for MATH32001 or MATH32200 depending on amount of time) in the upcoming academic year (2012/13). Other topics in areas such as spectral graph theory or computational number theory could also be possibilities; students are welcome to get in touch (via my magdt@bristol …
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These remarks started life as a series of short posts on Google+. But no-one uses Google+, so I’ve archived them here. I: you can make Voronoi diagrams using fine sand and blocks with holes drilled in. What’s a Voronoi diagram? In such an image, the plane is divided up into cells around sites, such that …
Continue reading ‘Neat things I learnt about at the Joint Math Meetings 2012’ »
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, …
A while ago I became interested in `captured lightning‘ Lichtenberg figures, but without access to megavolt-scale physics gear, I wondered if I could simulate them in software instead. I was reminded of this when I had my JMM art exhibition entry printed on glass, as this would give me something a bit closer to the …
I’ve been trying to extend the results of the work described in this post, and following a suggestion of Noam Elkies have changed my search strategy from points corresponding to simple EDS triples to those given by (A,u,c) parametrisations as described here. Experimenting with these revealed some serious deficiencies with the height function in SAGE, …
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I have uploaded a preprint of some recent efforts to the arXiv. In a break from my cyclotomic matrix work, this revisits a project I first became interested in over four years ago: the search for points with small height on elliptic curves over number fields, through the use of elliptic divisibility sequences. There used …
Continue reading ‘Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields’ »