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Zig-zags and statistics' bootstrap method, zig-zag persistence, other applications of zig-zag persistence
Visualizing data via homology' image statistics data, range patches, neuroscience
Topology & data: The future'
Topology and data
Topological methods for large and complex data sets
Speculations
Spaces 1: complexes' cech, v-rips, witnesses, alpha, etc. & uses in data
Representing Large and Complex Data
Persistent Homology and Applications
Persistence and point clouds' Functoriality, diagrams, difficulties in classifying diagrams, multidimensional persistence, Gröbner bases
Overview of Topological Data Analysis
Mapper for mapping' mapper as an imager. Importance of mapping. Applications of homology to mapping
Introduction to homotopy limits and colimits
Imaging data sets' linear regression, projection pursuit, multidimensional scaling as methods of imaging data sets
Homology 1' intro to homology simplicial, cellular, cech, & more: simple applications
Computing homology 2: practice' intro to algorithms/software; plex
Applied topology: motivations from data' point-set topology intro motivations from data, statistics, biology, etc.