Topological Analysis of Bone Microstructure, Directed Persistent Homology and the Persistent Laplacian for Data Science

In this talk, I will give an overview of recent joint work on Topological Data Analysis (TDA). The first one is an application of TDA to quantify porosity in pathological bone tissue. The second is an extension of persistent homology to directed simplicial complexes. Lastly, we present an evaluation of the persistent Laplacian in machine learning tasks. This is joint work with Ysanne Pritchard, Aikta Sharma, Claire Clarkin, Helen Ogden, and Sumeet Mahajan; David Mendez; and Tom Davies and Zhengchao Wang, respectively.