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Name: Andrew Thomas 

Talk Title: Functional strong laws of large numbers for Euler characteristic processes of extreme sample clouds

Abstract: In recent years, significant progress has been made in understanding the stochastic topology of noise. In particular, researchers have looked at how topological features behave when they are based off an increasing number of random points in Euclidean space lying at ever greater distances from the origin. In this talk, we will look at how the Euler characteristic of a filtration of random geometric simplicial complexes behaves when the points that generate them come from two distinct families of extreme value distributions. We will demonstrate a functional strong law of large numbers (FSLLN) for the Euler characteristic process—a summary of how this extremal topology evolves—in each distributional context. Based off of joint work with Takashi Owada.

This talk is an invited talk at EVA 2021. View the programme here.