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The (9ECM) is taking place from 15-19 July 2024, and the аĿª½±is exhibiting throughout. Come and find us at Booth 22 where you can speak to our Membership and Publications teams and find out more about the Society.

The аĿª½±Lecture will take place on 16 July 2024 with Professor Heather Harrington (University of Oxford) as our guest speaker. The аĿª½±Lecture is open to both members and non-members who are attending 9ECM.

Programme (all timings are in CEST)

Abstract: Persistent homology (PH) is a central tool in topological data analysis. PH provides a multiscale geometric descriptor of data that is functorial, stable to perturbations and interpretable, leading to many applications in mathematics and real-world data. Frequently one starts with point cloud data, a finite subset of a metric space (eg Euclidean space) and studies the topology arising from a filtration of simplicial complexes built on the data. While this process yields an interesting nontrivial descriptor of the "shape of data", some theoretical questions remain. In this talk, we will present two directions in application-driven point cloud persistence. First, we will focus on the spaces of point clouds with the same persistence. This inverse problem asks the following: What is the shape of the fiber of the persistent homology map? The second problem is motivated by spatial data arising in biology, which includes outliers (eg histology) or dynamic metric spaces (eg collective dynamics). We present statistics for multiparameter persistence and then apply it to complex biological data. To study these two PH directions, we adapt tools from applied and computational algebraic geometry.

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