On the Group of Real-Analytic Diffeomorphisms - Lecture 1

Watch a 67-minute mathematics lecture exploring the fundamental aspects of real-analytic diffeomorphisms and their role in manifold theory. Delve into the historical context of real-analytic manifolds and their study throughout the last century, examining how the discovery of partition of unity on smooth manifolds influenced the field. Learn about the natural automorphism group of real-analytic manifolds and understand why the absence of partition of unity by functions with support in balls creates unique challenges. Explore Herman's theorem regarding the simplicity of the identity component of real-analytic diffeomorphisms on the n-torus, setting the foundation for studying these groups on other manifolds. Recorded at the Centre International de Rencontres Mathématiques during the thematic meeting on Foliations and Diffeomorphism Groups, this lecture serves as the first in a series examining the fascinating properties and dynamics of real-analytic diffeomorphism groups.