Quantifying differences in shape via algebraic topology

Dr Katharine Turner, Senior Lecturer – Mathematical Sciences Institute, ANU


Dr Katharine Turner

The Australian National University

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

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

My other job is as mother to three children – each born on a different continent.


Wednesday, 10 January12pm - 1.30pm AEDTDr Katharine TurnerChina in the World, Building 188
Fellows Lane
The Australian National University

(Light refreshments provided)

Also broadcast over Zoom
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Talk 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 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.