Undergraduate Projects at the University of Bristol

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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Neat things I learnt about at the Joint Math Meetings 2012

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 …

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Updated: Lehmer’s conjecture for matrices over the ring of integers of some imaginary quadratic fields

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, …

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New records for integral multiples of points

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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Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields

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 …

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Cyclotomic Matrices and Graphs: Waterloo

I gave the Number Theory Seminar at the Department of Pure Mathematics, University of Waterloo on Thursday, September 8th. My slides are available in presentation or handout form (except the latter is missing the interlacing demo which didn’t render into individual slides correctly). I used this talk as an opportunity to present some results that …

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The Smoothness Spiral

I’d recently ordered Ben Fry‘s Visualizing Data and started reading it this weekend; just a few pages in I learnt how to import data to processing and a project was born… Since New Orleans I’ve been increasingly interested in mathematical art, and whether in particular I could create something interactive. Here’s what I’ve come up …

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