Breadcrumb
Lehmer's Conjecture for Weighted Graphs
Thu 07 March 2013, 16:30
Graeme Taylor
University of Bristol
Organisers: Tom McCourt, Tony Nixon, Karen Gunderson
ABSTRACT
I'll briefly discuss a number-theoretic problem, Lehmer's Conjecture, before re-casting it as a question about matrices with constrained eigenvalues. It turns out that a convenient way to think about these is via certain classes of weighted graphs - we'll look first at the rational integer case, then consider weights drawn from number fields. Throughout, we'll be interested in `cyclotomic' graphs - those with all eigenvalues in [-2,2] - and their extension to minimal non-cyclotomic graphs.