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Activity Number: 3
Type: Invited
Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract - #307444
Title: The Topology of Noise
Author(s): Omer Bobrowski*+
Companies: Duke University
Keywords:
Abstract:

A simplicial complex is a collection of vertices, edges, triangles, and simplexes of higher dimension, and one can think of it as a generalization of a graph. In a geometric complex, the presence of simplexes is determined by geometric properties of the vertices. Thus, choosing vertices at random yields a random topological space with many interesting features. We focus on the limiting behavior of the Betti numbers of such complexes, as the number of vertices goes to infinity. We present two different ways to study these random complexes, each yielding a completely different set of results and insights.


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