### GEORGE MASON
UNIVERSITY

DEPARTMENT OF MATHEMATICAL
SCIENCES

COLLOQUIUM

SEPTEMBER 5, 2014

**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.

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