Posts related to my research on Lehmer’s Mahler Measure problem – covers both cyclotomic and noncyclotomic matrices/graphs.
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 …
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 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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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 …
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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 …
Continue reading ‘Talks on Cyclotomic Matrices and Graphs’ »
Downloadable copy of my thesis.
Today I successfully defended my PhD thesis, Cyclotomic Matrices and Graphs. There are of course numerous corrections to be made, but I hope to have those done within the next couple of weeks and to make the final version available online. Until then, here is the abstract: We generalise the study of cyclotomic matrices – …
I’m back from the Fields Institute in Toronto, where I spoke at the above workshop, on my usual topic of cyclotomic and 4-cyclotomic matrices/graphs. During the talk I described my conjecture that a graph is maximal cyclotomic if-and-only if it’s 4-cyclotomic, and after an hour at the blackboards with James McKee I now have a …
Continue reading ‘Workshop on Discovery and Experimentation in Number Theory’ »