Introduction to topological data analysis

In this talk I’ll give a tour of how ideas and tools from topology are helping to provide important new methods of visualising, analysing, and exploring complex and high dimensional data sets.  I’ll describe the Mapper algorithm of Ayasdi and some of its applications, and then introduce persistent homology and discuss some of the ways it is getting used, both as a standalone tool, and as part of statistical analysis and machine learning pipelines.   This talk will be accessible to those with no previous exposure to data science; you need only know about open coverings, simplicial complexes, and homology.