Wednesday, October 1st, 2025 : 13:30 PM – 14.30 PM

Meeting Room 1, Department of Mathematics, Chiang Mai University

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The Department of Mathematics warmly invites faculty members, students, and all interested individuals to attend our monthly colloquium. Each session highlights advanced and engaging topics in mathematics presented by distinguished international speakers. This session, Prof. Dr. Sang-hyun Kim will give a talk on “Logical Structure of Diffeomorphism Groups.”

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ABSTRACT: Given a manifold $M$ and a structure $S$, we denote by $Homeo(M;S)$ the group of $M$-preserving homeomorphisms of $S$. We will be particularly concerned with the case that $S$ is the $C^r$ structure in the sense of Hölder continuity. In such a case, the group is written as $Diff^r(M)$.

The goal of this lecture is to survey recent results regarding the group theoretic structures and rigidity phenomena involving these groups. Concretely, we consider the question exactly when two manifold diffeomorphism groups $Diff^r(M)$ and $Diff^r(N)$ have the same logical structure.

Modern findings regarding this question give a generalization of classical results of Whittaker (1963), and of Takens–Filipkiewicz (1982). Joint work with Thomas Koberda (UVa) and Javier de la Nuez-González (KIAS).