Advances in Applied and Computational Topology

When recast into a computational setting, unrelated questions suchas: What is the shape of data? How do we describe flows? Can we count by integrating? How do we plan with uncertainty? become similar. Our input is a set of finite, discrete, noisy samples that describes an abstract space, and our goal is to compute qualitative features of the unknown space. It turns out that topology is sufficiently tolerant to provide us with robust tools. The aim of this volume is to provide a broad introduction to recent techniques from applied and computational topology.