Jerusalem Mathematics Colloquium

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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