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)

303 | AMA | February 2025

303 | AMA | February 2025

Welcome to the February 2025 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 Pa...

3 Helmi 20253h 44min

303 | James P. Allison on Fighting Cancer with the Immune System

303 | James P. Allison on Fighting Cancer with the Immune System

A typical human lifespan is approximately three billion heartbeats in duration. Lasting that long requires not only intrinsic stability, but an impressive capacity for self-repair. Nevertheless, thing...

27 Tammi 20251h 7min

302 | Chris Kempes on the Biophysics of Evolution

302 | Chris Kempes on the Biophysics of Evolution

Randomness plays an important role in the evolution of life (as my evil twin will tell you). But random doesn't mean arbitrary. Biological organisms are physical objects, after all, and subject to the...

20 Tammi 20251h 30min

301 | Tina Eliassi-Rad on Al, Networks, and Epistemic Instability

301 | Tina Eliassi-Rad on Al, Networks, and Epistemic Instability

Big data is ruling, or at least deeply infiltrating, all of modern existence. Unprecedented capacity for collecting and analyzing large amounts of data have given us a new generation of artificial int...

13 Tammi 20251h 9min

300 | Solo: Does Time Exist?

300 | Solo: Does Time Exist?

A new year, and a new centennial -- 300 (regularly-numbered) episodes of Mindscape! Our tradition is to have a solo episode, and what better topic than the nature of time? Physicists and philosophers ...

6 Tammi 20252h 11min

Holiday Message | Hits and Misses

Holiday Message | Hits and Misses

It's the end of the year, and time for our annual holiday break here at Mindscape. But as usual, we wrap up with a Holiday Message. This year, inspired by Joni Mitchell's "Hits" and "Misses" albums, I...

23 Joulu 20242h 1min

299 | Michael Wong on Information, Function, and the Origin of Life

299 | Michael Wong on Information, Function, and the Origin of Life

Living organisms seem exquisitely organized and complex, with features clearly adapted to serving certain functions needed to survive and procreate. Natural selection provides a compelling explanation...

16 Joulu 20241h 13min

298 | Jeff Lichtman on the Wiring Diagram of the Brain

298 | Jeff Lichtman on the Wiring Diagram of the Brain

The number of neurons in the human brain is comparable to the number of stars in the Milky Way galaxy. Unlike the stars, however, in the case of neurons the real action is in how they are directly con...

9 Joulu 20241h 9min

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