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)

279 | Ellen Langer on Mindfulness and the Body

279 | Ellen Langer on Mindfulness and the Body

For those of us who are not dualists, the mind arises from our physical bodies -- mostly the brain, but the rest of the body has a role to play. And yet it remains tempting to treat the mind as a thin...

17 Kesä 20241h 11min

278 | Kieran Healy on the Technology of Ranking People

278 | Kieran Healy on the Technology of Ranking People

We claim to love all of our children, friends, and students equally. But perhaps deep down you assign a ranking to them, from favorite to not-so-favorite. Ranking and quantifying people is an irresist...

10 Kesä 20241h 15min

AMA | June 2024

AMA | June 2024

Welcome to the June 2024 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreo...

3 Kesä 20243h 58min

277 | Cumrun Vafa on the Universe According to String Theory

277 | Cumrun Vafa on the Universe According to String Theory

String theory, the current leading candidate for a theory of quantum gravity as well as other particles and forces, doesn't connect directly to the world we see. It's possible that there is a large la...

27 Touko 20241h 22min

276 | Gavin Schmidt on Measuring, Predicting, and Protecting Our Climate

276 | Gavin Schmidt on Measuring, Predicting, and Protecting Our Climate

The Earth's climate keeps changing, largely due to the effects of human activity, and we haven't been doing enough to slow things down. Indeed, over the past year, global temperatures have been higher...

20 Touko 20241h 19min

275 | Solo: Quantum Fields, Particles, Forces, and Symmetries

275 | Solo: Quantum Fields, Particles, Forces, and Symmetries

Publication week! Say hello to Quanta and Fields, the second volume of the planned three-volume series The Biggest Ideas in the Universe. This volume covers quantum physics generally, but focuses espe...

13 Touko 20242h 12min

AMA | May 2024

AMA | May 2024

Welcome to the May 2024 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). We take questions asked by Patreon...

6 Touko 20243h 35min

274 | Gizem Gumuskaya on Building Robots from Human Cells

274 | Gizem Gumuskaya on Building Robots from Human Cells

Modern biology is advancing by leaps and bounds, not only in understanding how organisms work, but in learning how to modify them in interesting ways. One exciting frontier is the study of tiny "robot...

29 Huhti 20241h 10min

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