Colloquium: Dr. Joseph Rennie

(Higher) Categorical Galois Theory for the Aspiring Mathematician

Here we focus on the function/motivation of specific structures (most likely new to the audience) in high-level mathematics with the aim of highlighting major themes in the broader canvas of modern mathematics. Specifically, Galois Theoretic ideas emerge across disciplines, all as instances of a single theorem in (higher) category theory. This talk uses that idea to motivate a journey through three main themes relevant to any area:

1. The ubiquity of presheaf localizations
2. The concept of a classifying object
3. The pervasiveness of Algebro-Geometric duality

In some parts, I will use categorical-theoretic language not with the expectation that people speak the language, but rather as a demonstration of the beauty of the perspective gained by acquiring fluency. (What better way to motivate oneself to learn a new language than to listen to some of its poetry?)

This talk also serves as an onboarding for those interested in research projects on this topic. Though the talk should also inspire those who have no interest in category-theoretic research.