Title of the course: Borel equivalence relations and classification of countable mathematical structures
Instructor: Prof. Roman Kossak
Institution: The Graduate Center of the City University of New York
Dates: 22-28 September 2025
Prerequisites: An introductory course in topology would be helpful, but is not required. I will keep the lectures at a level suitable for beginners.
Level: Graduate, advanced undergraduate
Abstract: Countable mathematical structures such as countable ordered sets, graphs, groups, rings, fields, vector spaces, and many other can be represented as points in Polish topological spaces. Under this representation, the isomorphism relation in each given class of structures becomes a subset of a Polish space and this can be used to measure the complexity of those classes based on the set theoretic complexity of this relation. In recent years, it became a very active field of study. I will explain all basics of this approach and illustrate it with simple examples.
Language: English