H.B. Keller Colloquium

Historically, tools from algebraic topology are mathematically powerful but relatively inaccessible. In this talk, I will give an intuitive introduction to algebraic topology, with a focus on applying topological ideas to the study of people, geography, and physical space. My aim is to communicate some guiding principles and ideas that can be broadly applied to research across disciplines. As case studies, I will discuss applications to a variety of complex systems, including voting data, the organization of cities, and spiders on various psychotropic substances. Examples like these will be used to illustrate how mathematical notions of space coincide with and differ from physical ones, and how we can make use of these separate notions. This talk will be aimed at a broad mathematical audience.