turkmath.org

An important feature of modern science and engineering is that data of various kinds are being produced at an unprecedented rate. Topological Data Analysis (TDA) is a recent and fast-growing area providing a set of new topological and geometric tools to infer relevant features for possibly complex data. In this talk, we will give the definitions and properties of these tools, especially persistence homology, which algebraic topology is based and we show how it can be applied to particular data sets arising from natural image statistics and neuroscience. The talked is based on the paper 'Topology and Data' by Gunnar Carlsson.