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.


Jaksot(416)

168 | Anil Seth on Emergence, Information, and Consciousness

168 | Anil Seth on Emergence, Information, and Consciousness

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167 | Chiara Marletto on Constructor Theory, Physics, and Possibility

167 | Chiara Marletto on Constructor Theory, Physics, and Possibility

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166 | Betül Kaçar on Paleogenomics and Ancient Life

166 | Betül Kaçar on Paleogenomics and Ancient Life

In the question to understand the biology of life, we are (so far) limited to what happened here on Earth. That includes the diversity of biological organisms today, but also its entire past history. ...

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165 | Kathryn Paige Harden on Genetics, Luck, and Fairness

165 | Kathryn Paige Harden on Genetics, Luck, and Fairness

It's pretty clear that our genes affect, though they don't completely determine, who we grow up to be; children's physical and mental characteristics are not completely unrelated to those of their par...

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AMA | September 2021

AMA | September 2021

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164 | Herbert Gintis on Game Theory, Evolution, and Social Rationality

164 | Herbert Gintis on Game Theory, Evolution, and Social Rationality

How human beings behave is, for fairly evident reasons, a topic of intense interest to human beings. And yet, not only is there much we don't understand about human behavior, different academic discip...

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163 | Nigel Goldenfeld on Phase Transitions, Criticality, and Biology

163 | Nigel Goldenfeld on Phase Transitions, Criticality, and Biology

Physics is extremely good at describing simple systems with relatively few moving parts. Sadly, the world is not like that; many phenomena of interest are complex, with multiple interacting parts and ...

6 Syys 20211h 31min

162 | Leidy Klotz on Our Resistance to Subtractive Change

162 | Leidy Klotz on Our Resistance to Subtractive Change

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