Austin Shapiro
Introduction to polytopes
A convex polytope is...
- the n-dimensional analogue of a polygon or polyhedron
- a bounded intersection of finitely many half-spaces in R^n
- a bounded solution set for finitely many simultaneous linear inequalities
- the convex hull of finitely many points
I will give you a crash course on these objects and their basic properties,
including symmetry, Euler characteristic, face structure (f-vectors and
h-vectors), and other topics to be determined. The emphasis will be on
breadth rather than depth; many results will be stated and not proved, on
the grounds that one should have a look at the landscape before setting off
on a hunt. (This talk is the beginning of something approximating a series.)
First Abstract