Sheaves as a Data Structure

Abstract: The word “Topology”, best known for its association to the study of invariants of an abstract space, is a branch of Pure Mathematics whose best known applications are found in Physics (Quantum Mechanics, Quantum Field Theory). Very rarely does a Pure Math Field find such as Topology find relevance in a world of Big Data and computer automation. Data Science utilizes these powerful topological invariants to quickly gather information about complex data spaces in a brave new area of study called “Topological Data Analysis” or TDA. Given a set of data points, the nerve construction produces a simplicial complex that can be analyzed to understand important characteristics of the data. I will provide an introduction to TDA and a few examples of surprising Data Science applications.

mathematical physicsalgebraic topologycategory theory

Audience: researchers in the topic

Topology and Geometry Seminar (Texas, Kansas)