My third paper on the Mahler measure problem has been accepted by the Electronic Journal of Combinatorics, and is available here freely under the E-JC’s open access policy. This is joint work with Gary Greaves, and completes the proof of Lehmer’s conjecture for matrices with entries from rings of integers of quadratic extensions: a project …
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.
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, …
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, …
Continue reading ‘New records for integral multiples of points’ »
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’ »
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 …
Online access to my first paper.
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 …
Continue reading ‘Cyclotomic Matrices and Graphs: Warwick’ »
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 …