"Curvature of Polyhedra"
Abstract: The study of the curvature of polyhedra goes back to
Descartes. For a polyhedral surface M and a vertex v of
Mv is the angle defect, which is
2\pi minus the sum of the angles at v in the polygons
Descartes proved that the sum of the angle defects at the vertices
of a convex polyhedron in R^3 is 4\pi, which is a polyhedral analog
of the Gauss-Bonnet theorem.
This talk, which will be entirely elementary, will discuss some of
the geometric and combinatorial generalizations of the angle defect
to higher dimensions and to non-manifolds.