Algebraic degrees and Galois conjugates of pseudo-Anosov stretch factors

We consider questions that arise naturally from the subject of the first talk. The have two main results: 1. In genus $g$, the algebraic degrees of pseudo-Anosov stretch factors include all even numbers between $2$ and $6g - 6$; 2. The Galois conjugates of stretch factors arising from Penner’s construction are dense in the complex plane. The techniques may be characterized as asymptotic linear algebra.