B1008
Title: Random topology: A survey
Authors: Anthea Monod - Duke University (United States) [presenting]
Abstract: We give an overview of research topics stemming from applied and random topology, a relatively new field resulting from the application of point-set and algebraic topological methods to data that arise from random processes. The use of topological methods to analyze data is particularly applicable to information technology and networks (e.g. analyzing internet traffic and communications systems), physics (e.g. analyzing cosmological data), biology (e.g. brain imaging and studying gene regulation), and engineering (e.g. studying coordinated robotics). From the perspective of statistics, such methods are applicable to data mining and image processing. We outline the methodology of topological data analysis, and discuss recent results on the algebraic topology of random fields and complexes. We then present some problems that are currently being studied. In particular, we underline some contributions of applied topology to resolving statistical problems, and how statistical methodology can contribute to resolving applied topological problems.
