Exploring the Intersection of Category Theory & Differential Geometry 🧠

Talk given on February 16, 2022 on Zoom. Abstract: In this talk we will take a tour through some areas of math at the intersection of category theory and differential geometry. We will talk about how the use of category theory works towards solving 2 problems: 1) to give rigorous definitions and techniques to study increasingly complicated objects in differential geometry that are coming from physics, like orbifolds and bundle gerbes, and 2) to find good categories in which to embed the category of finite dimensional smooth manifolds, without losing too much geometric intuition. This involves the study of Lie groupoids, sheaves, diffeological spaces, stacks, and infinity stacks. I will try to motivate the use of these mathematical objects and how they help mathematicians understand differential geometry and expand its scope. Slides: https://drive.google.com/file/d/1JKAABeQlvrmTNekmZk_vYpKNpPbsa287/view?usp=sharing