How to 'See' the 4th Dimension with Topology

Video Description

Mathematician Maggie Miller explores the strange and fascinating world of 4D topology — the study of shapes, or manifolds, that resemble flat Euclidean space when viewed up close. Four-dimensional manifolds behave in unexpectedly complex ways, pushing mathematicians to develop advanced techniques to understand them. Maggie Miller is an assistant professor in the mathematics department at the University of Texas at Austin. She was also a former Visiting Clay Fellow and Stanford Science Fellow. -------- CHAPTERS 00:00 4D topology is weird 00:45 What is topology? 01:00 Manifolds 01:33 Examples of 1D manifolds 01:48 Examples of 2D manifolds 02:26 We live in a 3D manifold 03:05 4D manifolds explained 04:09 Why 4D topologists study 4D manifolds 05:11 4-torus manifold explained by analogy 10:28 Problems unique to 4D topology 10:44 Smooth vs continuous equivalency 12:04 Big open questions --------- - VISIT our website: https://www.quantamagazine.org - LIKE us on Facebook: / quantanews - FOLLOW us Twitter: / quantamagazine Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org