Explore topological data analysis and machine learning in this one-hour lecture by John Harer. Delve into key concepts including methodology, transformer examples, dimension reduction, and sliding windows. Learn about community-accepted features, extractors, binning, and syzygy coordinates. Examine machine learning with persistence through classification from local information and topological trackers. Investigate multi-scale local PCA and shape analysis techniques. Compare feature selections and discover methods for sorting and grabbing data. Gain insights into the intersection of topology and machine learning, enhancing your understanding of advanced data analysis techniques.