Speaker: Ezra Miller, Duke University

Title: Unfolding polyhedra

Abstract: Most of us as children saw those paper or cardboard cutouts, which we could call "foldouts", whose edges glue to form (boundaries of) 3-dimensional convex polyhedra. Just how did anyone figure out how to make them? Given a 3-dimensional convex polyhedron, does there always exist a foldout in the plane? What about higher dimensions? These questions have surprising answers, depending on the precise meaning of "foldout". One method is to treat boundaries of polyhedra like Riemannian manifolds. Algorithmic concerns then raise fundamental issues of computational complexity for the combinatorics of geodesics on polyhedra. Ideas from this work spill over into algorithms for doing statistics on spaces of phylogenetic trees and potentially lead to discrete versions of stratified Morse theory.

Place: Science and Technology Building I, Room 242

Refreshments will be served before the talk at 3:00 p.m. in Room 222.

Department of Mathematical Sciences
George Mason University
4400 University Drive, MS 3F2
Fairfax, VA 22030-4444
http://math.gmu.edu/
Tel. 703-993-1460, Fax. 703-993-1491