Milner 317

Wednesdays, 12:30-1:30 PM

Texas A&M University

**Wednesday, November 8
Milner 216, 12:30 PM**

**Title:** Lehmer's
conjecture, Salem numbers, and growth of groups

**Abstract:** Lehmer's
conjecture on the values of Mahler's measure of monic polynomials with
integer coefficients is closely connected to the so called minimization
problem for Salem numbers. In fact, any insight into the size of the
smallest possible Salem number would constitute a major step towards
Lehmer's conjecture. Salem numbers appear as largest poles of the
rational growth functions for certain Coxeter groups, and hence are
related to the asymptotic growth rates of these groups. This
fascinating connection, coming from the work of Cannon, E. Hironaka,
and others, provides additional evidence in support of Lehmer's
conjecture. I will review some results in this direction. This informal
expository talk can be viewed as a sequel to last week's talk by Jeff
Vaaler, however it will still be entirely self-contained with all
definitions and background information provided.