Alexandre Djerbetian (CS, Technion)
Shapes are usually described by their geometrical characteristics. Obviously, a rabbit doesn't look like a horse, because of its curvature for instance. However, some characteristics of a shape are independent of its geometry. A rugby ball is still a ball, and a doughnut looks like a tire. Those are called topological features of the shape, and homology is one the tool that mathematicians use to separate a sphere from a torus. A rabbit being equivalent to a horse, this often makes topology be a neglected tool in computer science for obvious reasons. However, some topological knowledge can sometimes help us have a better understanding of the underlying shape, behind the geometry, and then help make meaningful topological simplification. In this talk, I will introduce the concept and the algorithm of persistent homology, a tool to classify the importance of the topological features of arbitrary shapes. We will for instance count the number of mountains and valleys in a given geography, and sort them by topological importance.