Mathematics Colloquium: The discrete Morse theory of Cech and Delaunay complexes.

Speaker: Herbert Edelsbrunner, IST Austria

Title: The discrete Morse theory of Cech and Delaunay complexes.

Abstract: Given a finite set of points in R^n, we consider the filtrations of Cech and alpha complexes and show that they define generalized discrete Morse functions on the complete simplicial complex and the Delaunay triangulation. We use this insight to prove that the Cech complex for a given radius collapses to the alpha complex for the same radius. Among other things, these results imply an extension of the wrap algorithm for shape reconstruction,

This is joint work with Ulrich Bauer.

Time: Friday, September 5, 2014, 3:30-4:20 p.m.

Place: Exploratory Hall, room 4106

Refreshments will be served at 3:00 p.m.