Workshop on Topology: Identifying Order in Complex Systems

In this talk, I will try to explain some of the interest in the question of the computation of the homology of a space from noisy data samples as it relates to clustering and other natural problems. Moreover, I will also try to indicate some applications to dynamics. The analysis I will give is based on joint work with Partha Niyogi (CS and Statistics, U of C) and Steve Smale (TTI-C) and related work with Yuliy Baryshnikov (Bell Labs).