Event: Public Lecture
Title: Quantifying Differences in Shape via Algebraic Topology
Speaker: Katharine Turner, ANU
Date/Time: Wednesday 10 January 2024; 12–1.30pm AEDT
Location: China in the World, Building 188, Fellows Road, ANU
Homology is an algebraic invariant of the topology of a space. A single homology measurement cannot distinguish subsets of Euclidean space that are topologically the same but geometrically different. However, by considering a parameterised families of growing subsets of a shape and how the homology evolves over this families (called persistent homology) we can bridge between the topological and geometric. I will talk about how we can use persistent homology to construct a metric between different subsets of Euclidean space and give some examples of applications from classification of serif from sans serif fonts, to disease prognosis of brain tumours.