Connect the dots: from data through complexes to persistent homology

Abstract: In this talk, I will survey some recent results on theoretical and computational aspects of applied topology. I will illustrate various aspects of persistent homology: its structure, which serves as a topological descriptor, its stability with respect to perturbations of the data, its computation on a large scale, and connections to Morse theory.

These aspects will be motivated and illustrated by concrete examples and applications, such as

* reconstruction of a shape and its homology from a point cloud,

* faithful simplification of contours of a real-valued function,

* existence of unstable minimal surfaces, and

* identification of recurrent mutations in the evolution of COVID-19.

algebraic topologycategory theory

Audience: researchers in the topic

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Bilkent Topology Seminar

Series comments: Contact the organizer to get access to Zoom.

Recordings of talks available at www.youtube.com/channel/UCLrmyGpqxyeVpTcA1b5HcMw/videos

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