The field of algebraic topology focuses on studying topology, or shape, using algebraic concepts such as homology and homotopy groups. A comparatively recent addition to this literature has been the notion of persistent homology, which turns out to be useful for picking out global features of complicated structures. This has lead to the growing area of “topological data analysis” which has brought together topologists, engineers, and, even more recently, statisticians. Probabilists are now also joining the fray. I will describe some of these ideas, using problems in random processes as a vehicle, as well as describing some new results. No background in topology, statistics, or random processes will be assumed. Everything will be explained online, with lots of pictures.
About the speaker: Robert Adler is Professor at the Faculty of Electrical Engineering at Technion, Haifa, Israel. He also holds the Louis and Samuel Seiden Technion Academic Chair. His versatile research interests include: the study and application of random fields, extremal theory of Gaussian processes and fields, Superprocesses as continuum models for infinitely many particles undergoing both diffusion and branching, and random processes on manifolds.