Marcus Tressl

Non-Hausdorff Topology in Algebra and Logic

This course will give an introduction to spectral spaces focussing on

Topological representation theory of posets, starting with Stone Duality, including Priestley duality.
Coding of logical axioms (e.g. intuitionistic logic, modal logic) as topological properties of spaces.
Connections to other categories, specifically topological spaces, frames and commutative rings.

We will assume familiarity with a few elementary notions from category theory (like functors and natural transformations) and set theoretic topology (like continuous functions and compact spaces). The main reference for the course is the book

M. Dickmann, N. Schwartz, M. Tressl; Spectral Spaces. New Mathematical Monographs, vol. 35. Cambridge University Press. March 2019. https://doi.org/10.1017/9781316543870