Join us for a public lecture from Associate Professor Kate Turner from the Mathematics Sciences Institute at ANU. A light lunch will be served beforehand.

Abstract

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 consider 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.

About the speaker

Kate Turner's passion is turning pure mathematics into practical ways to understand the world. Her approach spans proving theorems in algebraic topology, to developing statistical methods, to analysing data in diverse applications.

Born and bred in Sydney, she studied pure mathematics at the University of Sydney. During her PhD at the University of Chicago she discovered Topological Data Analysis; an innovative field mixing pure and applied mathematics. In a joint postdoc at École Polytechnique Fédérale de Lausanne (EPFL, Switzerland) she bridged the Mathematical Statistics group and the Laboratory for Topology and Neuroscience. In 2017 she returned to Australia, joining the Mathematical Sciences Institute (MSI) at ANU.

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Topic: Quantifying differences in shape via algebraic topology. A public lecture with Kate Turner.

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