Random Topology : A Survey.

~~
In this talk, I will 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.
I will outline the methodology of topological data analysis, and discuss recent results on the algebraic topology of random fields and complexes.  I will then present some problems that are currently being studied.  In particular, I will underline some contributions of applied topology to resolving statistical problems, and how statistical methodology can contribute to resolving applied topological problems.