Countable Subgroups of Homeomorphism Groups: Dimension One and Beyond - Lecture 3

Explore the intricacies of countable subgroups within homeomorphism groups in this advanced mathematics lecture. Delve into the complexities of dimension one and beyond, focusing on regularity in one-dimensional scenarios. Examine the collaborative work with S. Kim on critical regularity and discover the outline of a program aimed at generalizing one-dimensional results to higher dimensions. Gain insights into recent findings on the model theory of homeomorphism groups of compact manifolds, developed in conjunction with S. Kim and J. de la Nuez Gonzalez. Consider potential future generalizations of these concepts and their implications for the field of mathematics.