Topology

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Topology is the study of spaces, both em you know, kind of physical, geometrical spaces that we move in in the world. You could imagine the points on a plane as an example of a topological space. M, or you can imagine the points that are on the surface of a doughnut. And then you can start to compare what those worlds are, liketopologies a realm to do that? Emmy, why don't i rathe than try to guess? Why don't you tell us what you think the definition of topology is that we could all get our hands on?

“A way that math can make the world a better place is by making it a more interesting place to be a conscious being.” So says mathematician Emily Riehl near the start of this episode, and it’s a good summary of what’s to come. Emily works in realms of topology and category theory that are far away from practical applications, or even to some non-practical areas of theoretical physics. But they help us think about what is possible and how everything fits together, and what’s more interesting than that? We talk about what topology is, the specific example of homotopy — how things deform into other things — and how thinking about that leads us into groups, rings, groupoids, and ultimately to category theory, the most abstract of them all.

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Emily Riehl received a Ph.D in mathematics from the University of Chicago. She is currently an associate professor of mathematics at Johns Hopkins University. Among her honors are the JHU President’s Frontier Award and the Joan & Joseph Birman Research Prize. She is author of Categorical Homotopy Theory, and co-author of the upcoming Elements of ∞-Category Theory. She competed on the United States women’s national Australian rules football team, where she served as vice-captain.

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