##### Speaker

Dr. Paul Fabel, Associate Professor, Department of Mathematics and Statistics, MSU

##### Title

Mathematics Seminar Series

##### Subtitle

How are connected finite topological spaces fundamental to data science?

##### Physical Location

Allen 411

“Everything is a space and all functions are continuous''. The previous slogan is fundamental to both topology and theoretical computer science.

This talk aims to promote the slogan as useful in data science and in particular to computational topological data analysis, in the context of finite T_0 spaces, as useful simplicial approximations to more general spaces X.

To illustrate the ideas we will explore very simple examples, with a main goal of providing a precise and useful answer to the following general puzzle.

Suppose X is a familiar ``nice'' space such as [0,1]. We will show how to construct a sequence of finite topological spaces K_{n} and CONTINUOUS maps F: [0,1]-->K_{n} so that we may recover X as the inverse limit. The oft overlooked and under-used T_{0} separation is exactly what will help us solve the mentioned puzzle in a nice way.

This construction lies at the heart of both computational topology, and serves as a tool to model finite data sets with finite path connected spaces.