Topological Data Analysis is a relatively new field of research that seeks to bring powerful tools from algebraic topology to bear on practical problems in data science (where statistics has been the more traditional toolset). This talk, by Dr. Leland McInnes from the Tutte Institute for Mathematics and Computing, will begin by using topological methods to construct a new approach to dimension reduction, and then build out the theory to provide new approaches to clustering and anomaly detection. Our goal is to provide a unified topological approach to unsupervised learning.