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Celia Hacker: Signal processing on cell complexes with discrete Morse theory

Tid: Ti 2022-05-31 kl 10.15

Plats: KTH, 3721, Lindstedtsvägen 25, and Zoom

Videolänk: Meeting ID: 659 3743 5667

Föreläsare: Celia Hacker (EPFL)

Abstract

At the intersection of Topological Data Analysis and machine learning, the field of cellular signal processing has advanced rapidly in recent years. In this context, each signal on the cells of a complex is processed using the combinatorial Laplacian and the resulting Hodge decomposition. Meanwhile, discrete Morse theory has been widely used to speed up computations by reducing the size of complexes while preserving their global topological properties. In this talk, we introduce an approach to signal compression and reconstruction on complexes that leverages the tools of discrete Morse theory. The main goal is to reduce and reconstruct a cell complex together with a set of signals on its cells while preserving their global topological structure as much as possible.

This is joint work with Stefania Ebli and Kelly Maggs.