146 | Emily Riehl on Topology, Categories, and the Future of Mathematics

146 | Emily Riehl on Topology, Categories, and the Future of Mathematics

"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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Holiday Message 2019: On Publishing Books

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18 Nov 20191h 18min

72 | César Hidalgo on Information in Societies, Economies, and the Universe

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Maxwell's Demon is a famous thought experiment in which a mischievous imp uses knowledge of the velocities of gas molecules in a box to decrease the entropy of the gas, which could then be used to do ...

11 Nov 20191h 16min

71 | Philip Goff on Consciousness Everywhere

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The human brain contains roughly 85 billion neurons, wired together in an extraordinarily complex network of interconnected parts. It's hardly surprising that we don't understand the mind and how it w...

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