Explore persistent entropy as a tool for topologically summarizing data in this 52-minute conference talk. Delve into the properties and applications of this entropy-based summarization of persistence barcodes, including its stability to small perturbations in input data. Learn about its usefulness in machine learning and pattern recognition. Discover diverse applications such as emotion recognition in talking-face videos, summarizing cell organization in epithelial tissues, and characterizing literary styles of poets. Gain insights into the persistent entropy formula, normalization techniques, and stability properties. Examine practical examples in emotion recognition, epithelial tissue analysis, and philology using word embeddings. Conclude with a summary of applications and engage in a Q&A session addressing intuitive interpretations of persistent entropy.