AI3SD Video: Topology: From shapes to numbers

Topology is a branch of mathematics that concerns itself with a study of shape and how to describe them through computable numerical characteristics. While this sounds inauspicious, in the last two decades we witnessed a very rapid development of Topological Data Analysis (TDA), which has now established itself as a key part of modern data-driven science alongside machine learning and statistics. There are now very many examples of how TDA can be used to derive information from complex data sets and to provide insight into complex scientific problems. In this talk, we will introduce the main tools of TDA and to illustrate their applications to the problem of solubility of chemical compounds. The talk will also serve as an introduction to the other talks in this session.