The Biggest Ideas in the Universe is a series of videos where I talk informally about some of the fundamental concepts that help us understand our natural world. Exceedingly casual, not overly polished, and meant for absolutely everybody. This is the Q&A video for Idea #13, "Geometry and Topology." We use the excuse to dig into some details of embeddings, how to express the Riemann tensor, what maps are involved in specifying homotopy groups, plus a bit about topological defects. My web page: http://www.preposterousuniverse.com/ My YouTube channel: https://www.youtube.com/c/seancarroll Mindscape podcast: http://www.preposterousuniverse.com/podcast The Biggest Ideas playlist: https://www.youtube.com/playlist?list=PLrxfgDEc2NxZJcWcrxH3jyjUUrJlnoyzX Blog posts for the series: http://www.preposterousuniverse.com/blog/category/biggest-ideas-in-the-universe/ Background image by RyoThorn at DeviantArt: https://www.deviantart.com/ryothorn/art/Steamworks-to-my-own-oblivion-147929840 #science #physics #ideas #universe #learning #cosmology #philosophy #math #geometry #topology