The field of topological data analysis is still quite young. We will give an introduction, look at some applications, and discuss theoretical challenges. Beyond some basic linear algebra, little previous knowledge will be assumed.

* BioSketch*: Prof Tillman is a renown algebraic topologist who has made important contributions to the study of the moduli space of algebraic curves. She has been the founding and managing editor of Journal of Topology from 2007-2017.

She is Professor at the Mathematical Institute of Oxford University since 2010. For her results she has received many recognitions among which the Whitehead Prize from the London Mathematical Society in 2004. She was elected Fellow of the Royal Society in 2008 and Inaugural Fellow of the American Mathematical Society in 2012. She has been invited speaker at ICM 2002.

She is director of the Newton Institute in Cambridge, president of the London Mathematical Society and vice-president of the International Mathematics Union.