Katharine Turner, Persistent homology rank function

Speaker: Dr Katharine Turner
Australian National University
Title: Persistent homology rank function
Date and time: Monday 13 November 2017, 10:30am
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract:
Persistent homology is a tool for capturing how topological features evolve over an increasing family of spaces. Commonly these spaces are taken to be the unions of balls of increasing radii about some finite set of points. Using this scaling parameter we can summarise geometric information as a topological summary statistic. In this talk I will introduce persistent homology and define the persistent homology rank function which, as a functional summary lying in a Hilbert space, enables us to perform statistical analysis such as principal component analysis. I will present some applications including testing complete spatial randomness of spatial point patterns, and comparing experimental sphere packings and colloid data under different temperatures. This talk is based on work with Vanessa Robins.

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