Speaker: Gunter Ziegler
Title: Spaces of $f$-vectors of polytopes
In 1906, Ernst Steinitz described the set of all
face-vectors of $3$-dimensional polytopes as the set
of all integer points in a certain cone, whose apex
corresponds to the $3$-simplex.
This result may be seen as the starting point for
similar investigations treating
polytopes of dimension $d\ge4$,
flag vectors,
centrally symmetric polytopes.
We will survey the current state of knowledge:
Many fundamental questions remain open (and challenging),
but there are also recent results and new ideas to report about.