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)

AMA | July 2021

AMA | July 2021

Welcome to the July 2021 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). I take the large number of questi...

9 Heinä 20213h 49min

154 | Reza Aslan on Religion, Metaphor, and Meaning

154 | Reza Aslan on Religion, Metaphor, and Meaning

Religion is an important part of the lives of billions of people around the world, but what religious belief actually amounts to can vary considerably from person to person. Some believe in an anthrop...

5 Heinä 20211h 25min

153 | John Preskill on Quantum Computers and What They're Good For

153 | John Preskill on Quantum Computers and What They're Good For

Depending on who you listen to, quantum computers are either the biggest technological change coming down the road or just another overhyped bubble. Today we're talking with a good person to listen to...

28 Kesä 20211h 32min

152 | Charis Kubrin on Criminology, Incarceration, and Hip-Hop

152 | Charis Kubrin on Criminology, Incarceration, and Hip-Hop

It's all well and good to talk abstractly about morality and justice, but at some point you have to sit down and figure out what to do about people who break the rules. In our modern legal system, mos...

21 Kesä 20211h 19min

151 | Jordan Ellenberg on the Mathematics of Political Boundaries

151 | Jordan Ellenberg on the Mathematics of Political Boundaries

Any system in which politicians represent geographical districts with boundaries chosen by the politicians themselves is vulnerable to gerrymandering: carving up districts to increase the amount of se...

14 Kesä 20211h 23min

AMA | June 2021

AMA | June 2021

Welcome to the June 2021 Ask Me Anything episode of Mindscape! These monthly excursions are funded by Patreon supporters (who are also the ones asking the questions). I take the large number of questi...

10 Kesä 20213h 18min

150 | Simon DeDeo on How Explanations Work and Why They Sometimes Fail

150 | Simon DeDeo on How Explanations Work and Why They Sometimes Fail

You observe a phenomenon, and come up with an explanation for it. That's true for scientists, but also for literally every person. (Why won't my car start? I bet it's out of gas.) But there are litera...

7 Kesä 20211h 32min

149 | Lee Smolin on Time, Philosophy, and the Nature of Reality

149 | Lee Smolin on Time, Philosophy, and the Nature of Reality

The challenge to a theoretical physicist pushing beyond our best current theories is that there are too many ways to go. What parts of the existing paradigm do you keep, which do you discard, and why ...

31 Touko 20211h 29min

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