SAMS Subject Classification Number: 23

Topological Data Analysis (TDA) is a novel, and relatively new approach to analysing high-dimensional data sets. It does this by fo- cussing on global properties like the shape and connectivity of the data giving it a significant advantage over more conventional tools based on cluster analysis, a localised property of the data. However, some of its mathematical foundations, like algebraic topology and discrete Morse theory, are perceived as an intimidatingly steep upramp into the subject. Consequently, it has enjoyed much less popularity as a data-analysis tool than less abstract methods. This talk will give an introduction to this fascinating subject by focusing on a small set of simple examples, chosen primarily for their pedagogical value. I will illustrate the universality of the method by discussing two applications: 1. to the intriguing data set of fast radio burst (FRB) observations in astrophysics and 2. to the study of quantum phase transitions in condensed matter physics.

Bio: Jeff Murugan is Professor of Mathematical Physics at the University of Cape Town (UCT). Prof Murugan was a postdoctoral fellow in Brown University’s High Energy Theory group, a member of the School of Natural Sciences of the Institute for Advanced Study in Princeton, a Research Associate in the Division of Physical Sciences at the American Museum of Natural History in New York, and a Simons Associate at the International Center for Theoretical Physics in Trieste.

A String Theorist by training, his work currently lies at the nexus of quantum information and quantum matter where he is one of the co-discoverers of the 3-dimensional web of dualities and, together with Douglas Stanford and Edward Witten, is in the MSW class of disordered conformal field theories. He is also the recipient of UCT’s Distinguished Teacher Award for 2018.