  For a simplicial complex or more generally Boolean cell complex $\Delta$ we
study the behavior of the $f$- and $h$-vector under barycentric subdivision. We
show that if $\Delta$ has a non-negative $h$-vector then the $h$-polynomial of
its barycentric subdivision has only simple and real zeros. As a consequence
this implies a strong version of the Charney-Davis conjecture for spheres that
are the subdivision of a Boolean cell complex.
  For a general $(d-1)$-dimensional simplicial complex $\Delta$ the
$h$-polynomial of its $n$-th iterated subdivision shows convergent behavior.
More precisely, we show that among the zeros of this $h$-polynomial there is
one converging to infinity and the other $d-1$ converge to a set of $d-1$ real
numbers which only depends on $d$.
