Gunnar Carlsson: The shape of data

In recent years, it has become possible to collect very large amount of data of extremely varied types. Analyzing these data sets is a problem which is now recognized as one of the fundamental intellectual problems facing the scientific and mathematical communities. Topology can be characterized as the study of shape, and most data sets are equipped with a notion of shape, via a metric which captures the notion of similarity of data points. From this observation, one can attempt to adapt topological methods to studying these data. In this talk, I will present some of these methods, with examples.

This lecture is aimed at a general audience interested in applied topology. It is aimed particularly to those specializing in biological/medical sciences, computer vision and robotics whose work requires analysis of big data sets.