The geometry of convex polyhedra

I will start by discussing various geometric and
computational problems on surfaces of convex
polyhedra related to computing the geodesic
distance, non-overlapping unfolding, isometric
embeddings of surfaces, etc. I will try put these
results into historical perspective, by showing
connections to the smooth case as a motivation.
In the second part of the talk I will outline my
joint work with Ezra Miller on non-overlapping
unfoldings of convex polyhedra in higher dimension,
and how these can be obtained algorithmically by
using the cut locus construction.