Course Title: Fundamental Groups and Category Theory
Speaker: Andrey Lazarev, Lancaster University
Location: The Fifth Seminar Room, Mathematics Building, Jilin University
Abstract: This course introduces some basic concepts of category theory, such as natural constructions (functors) and equivalence of categories. The category of sets with a group action will be studied as an example. This category is then related to the category of covering spaces over a given topological space (this part requires familiarity with, or acceptance of, some results from Minicourse 1). If time permits, an outline of Galois theory viewed as an equivalence of categories will be provided.
14:30–15:30, July 6, 2025 – Categories, functors and equivalence of categories
14:30–15:30, July 7, 2025 – The category of sets with a group action. Orbits and stabilizers
14:30–15:30, July 8, 2025 – Classification of covering spaces as an equivalence of categories
14:30–15:30, July 9, 2025 – Outline of Galois theory as an equivalence of categories. Analogy with covering spaces
Speaker Biography: Andrey Lazarev is a Professor at Lancaster University, UK. His research focuses on algebraic topology and homotopy theory. He has served as Editor-in-Chief of the Bulletin of the London Mathematical Society and has published numerous high-level papers in journals including Advances in Mathematics, Proceedings of the London Mathematical Society, and Journal of Noncommutative Geometry.
