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Friday, April 18, 2014

**Abstract:** Topological data analysis is a relatively new field that seeks to apply techniques from algebraic topology to problems that have traditionally been approached using statistical methods. One such problem is as follows: Given a set of points sampled randomly from a space $X$, can one recover the topological structure of $X$? A key technique that has been developed to address this question is persistent homology. We will give an introduction to this technique and compare different ways of presenting the resulting information, such as barcodes, persistence diagrams, and merge trees.