The Memory of Persistence

As we pass the 20th anniversary of persistent homology and the 10th anniversary of the deep learning revolution, it is time to take stock. In this talk, I will look back and discuss some of the milestones, i.e. work that embodies the intricate interplay of geometry, topology, and machine learning techniques, with a particular eye towards applications. I hope to convince the audience that, indeed, there is an unreasonable effectiveness to topological methods in general and persistent homology in particular. Next to this retrospective, I will also outline areas of improvement and 'unmet needs', with the goal of providing a vision for an even better future. To this end, I will highlight new research directions that aim to advance geometry, topology, and machine learning.