Thursday, 3rd July 2008, 4:00 pm

Mathematics Building, Lecture Hall 2

Ethan Bloch

(Bard College)

"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
containing *v*.
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.

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