Oscar Randal-Williams (University of Cambridge) gives a lecture titled "Symmetries of Manifolds" as part of the 2024 Unni Namboodiri Lectures in Geometry and Topology.

Abstract:
Whenever one studies a mathematical object one ought also to study its symmetries. Manifolds---spaces which look locally like ordinary Euclidean space but which can be globally complicated---are the central objects of study in topology and geometry, and their groups of symmetries come in many flavours (isometries, diffeomorphisms, homeomorphisms, ...). In this course of lectures I will discuss some classical and recent results about the spaces of all symmetries of simple manifolds---such as the sphere, the disc, or Euclidean space---give some ideas of the recent methods which have been to study them, and report on an emerging conjectural picture.