Kevin Sweet

You may have heard the phrase “a topologist cannot tell the difference between a donut and a coffee mug.” This is because a donut and a coffee mug are topologically equivalent: they can be stretched into the same shape. Homology
is a topological invariant that can be used to differentiate different shapes, but what happens when we start with a collection of data points instead of a complete topological object? Persistent homology is a technique for generating homology groups from a point cloud of data. In this talk, I will cover the basic ideas of simplicial homology and persistent homology, and then explore some of the applications of persistent homology to musical data such as pitches, chords and rhythms.