 
Summary: Dynamics on algebraic surfaces
MPI Arbeitstagung 2007
Curtis T. McMullen
In this talk we discuss connections between algebraic integers and auto
morphisms of compact complex surfaces.
Integers. Conjecturally, the smallest algebraic integer > 1 is the root
Lehmer = 1.1762808 . . . of Lehmer's polynomial,
P(x) = 1 + x  x3
 x4
 x5
 x6
 x7
+ x9
+ x10
.
By smallest we mean the Mahler measure, given by the product of the
conjugates of outside the unit disk, is minimized. In fact Lehmer is a
Salem number: it is the unique root of P(x) outside the disk, so it is its own
Mahler measure.
Lehmer's polynomial has several geometric manifestations; especially, it
