UNLV Mathematical Sciences
2007-2008 Colloquium

The Markoff equation and a conjecture of Frobenius


Dr. Arthur Baragar
Department of Mathematical Sciences
UNLV



Abstract

In this talk, we investigate the Diophantine equation
x2+y2+z2=3xyz
whose integer solutions are connected to Diophantine approximation, quadratic bilinear forms, and minimal geodesics on a puctured torus. We will discuss some outstanding questions with respect to this equation and similar equations, some of which could lead to thesis topics, and a conjecture of Frobenius that has been around for almost a century.