Gandalf (Pure Maths Student Seminar): Lehmer's conjecture and hyperbolic geometry
7 March 2012 16:15 in CM107Given a monic integral polynomial p, one may define its Mahler measure as the product of all its roots with absolute value at least 1. The smallest known Mahler measure is for a polynomial of degree 10, and Lehmer's problem is to find a smaller Mahler measure; the conjecture is that one cannot. The truth of the conjecture would imply another conjecture, known as the Short Geodesic Conjecture hyperbolic geometry. I will explain some of these ideas and how they relate to some of my own work (joint with M. Belolipetsky).
Gandalf is the pure maths student seminar. Gandalf stands for the Geometry AND ALgebra Forum. It is run by and for pure postgraduates, but welcomes anyone who is interested in coming along.
Content from previous talks is available at the gandalf seminar home page.