{TALK
{"September 16}
{"Inequalities for the CD-Index}
{"Richard Ehrenborg}
{"Institute for Advanced Study}
{"}
{"
We prove an inequality involving the cd-indices of a convex polytope
P, a face F of the polytope and the link P/F. As a consequence we
settle a conjecture of Stanley that the cd-index of d-dimensional
polytopes is minimized on the d-dimensional simplex. Moreover, we show
how this gives quadratic inequalities on the flag f-vector of
polytopes. Lastly, we present an upper bound theorem for the cd-index
of polytopes.}
}