Applied Topology Seminar - "A directed persistent homology theory for dissimilarity functions"

The first Applied Topology Seminar of this year will be held online on Tuesday, the 22nd of September at 15:15.

Zoom link:  https://epfl.zoom.us/j/96240198275

Speaker: David Mendez, University of Southampton

Title: A directed persistent homology theory for dissimilarity functions

Abstact: Persistent homology is one of the most successful tools in Topological Data Analysis, having been applied in numerous scientific domains such as medicine, neuroscience, robotics, and many others. However, a fundamental limitation of persistent homology is its inability to incorporate directionality.
In this talk we will introduce a theory of persistent homology for directed simplicial complexes which detects directed cycles in odd dimensions. To do so, we introduce a homology theory with coefficients in semirings for these complexes: by explicitly removing additive inverses, we can detect directed cycles algebraically. We will also exhibit some of the features of this persistent homology theory, including its stability and how the obtained persistent diagrams relate to those obtained from persistent homology with ring coefficients. We will end the talk by highlighting some of the computational challenges towards the effective computation of the directed persistent diagram of a pointcloud.

More information on the seminar's webpage: https://www.epfl.ch/labs/hessbellwald-lab/seminar/apptopsem2021/#mendez