Explore efficient computation of Vietoris–Rips persistence barcodes in this 51-minute lecture from the Hausdorff Trimester Program on Applied and Computational Algebraic Topology. Delve into Ripser, a compact C++ software for calculating persistence barcodes, and its design goals. Examine matrix reduction algorithms, persistent cohomology, and the fundamental theorem of discrete Morse theory. Learn about Morse pairs, persistence pairs, and apparent pairs, connecting Morse theory to persistence. Gain insights into Vietoris-Rips filtrations, compatible basis cycles, and oblivious matrix reduction techniques. Witness a live demonstration of Ripser's global reach, showcasing users from 156 different cities.