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 Postdoc category.
New records for integral multiples of points
I’ve been trying to extend the results of the work described in the previous 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 [...]
Nontorsion Points of Low Height on Elliptic Curves over Quadratic Fields
I have uploaded a preprint of my third paper 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 [...]
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 [...]
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 [...]
Bristol (and beyond?)
It’s almost September, although I’m not entirely sure how: feels like I’ve just started at Bristol, yet today marks three months here! So I’ve signed up for a couple of local events in September: the Heilbronn annual conference 2010 is on the 16-17th, and Engage 2010 is the following week, on the 23rd. Less concretely, [...]
