Approximating data sets by graphs and simplicial complexes has been shown to be a very useful way to obtain qualitative information about data, and more recently has been shown to similarly contribute to artificial intelligence.  I will discuss the mathematics around this, with examples from various domains.  

BIO: Gunnar Carlsson is the Ann and Bill Swindells Professor Professor of Mathematics, Emeritus, at Stanford University, and a pioneer in the field of computational topology. His research focuses on the application of topological methods  to the analysis of high-dimensional, complex data, a discipline known as Topological Data Analysis (TDA). Professor Carlsson is perhaps best known for leading the "Topological Methods in Data Analysis" project (supported by DARPA), which catalyzed the development of persistent homology and mapper algorithms. Beyond his academic contributions, he co-founded Ayasdi, a company dedicated to utilizing TDA for industrial-scale machine learning and data science. He holds a Ph.D. from Stanford and has previously held faculty positions at the University of Chicago, the University of California, San Diego, and Princeton University.