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.

Support Mindscape on Patreon.

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.


Det här avsnittet är hämtat från ett öppet RSS-flöde och publiceras inte av Podme. Det kan innehålla reklam.

Avsnitt(427)

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...

13 Sep 20211h 29min

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 Sep 20211h 31min

162 | Leidy Klotz on Our Resistance to Subtractive Change

162 | Leidy Klotz on Our Resistance to Subtractive Change

There is no general theory of problem-solving, or even a reliable set of principles that will usually work. It's therefore interesting to see how our brains actually go about solving problems. Here's ...

30 Aug 20211h 14min

161 | W. Brian Arthur on Complexity Economics

161 | W. Brian Arthur on Complexity Economics

Economies in the modern world are incredibly complex systems. But when we sit down to think about them in quantitative ways, it's natural to keep things simple at first. We look for reliable relations...

23 Aug 20211h 35min

160 | Edward Slingerland on Confucianism, Daoism, and Wu Wei

160 | Edward Slingerland on Confucianism, Daoism, and Wu Wei

Plato and Aristotle founded much of what we think of as Western philosophy during the fourth and fifth centuries BCE. Interestingly, that historical period also witnessed the foundation of some of the...

16 Aug 20211h 23min

AMA | August 2021

AMA | August 2021

Welcome to the August 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 ques...

12 Aug 20213h 11min

159 | Mari Ruti on Lack, Love, and Psychoanalysis

159 | Mari Ruti on Lack, Love, and Psychoanalysis

Neuroscience has given us great insights into how our brains work. But there is still room for purely humanistic disciplines to help us think through our thoughts and emotions, not to mention the mean...

9 Aug 20211h 49min

158 | David Wallace on the Arrow of Time

158 | David Wallace on the Arrow of Time

The arrow of time — all the ways in which the past differs from the future — is a fascinating subject because it connects everyday phenomena (memory, aging, cause and effect) to deep questions in phys...

2 Aug 20211h 47min

Populärt inom Vetenskap

dumma-manniskor
allt-du-velat-veta
p3-dystopia
kapitalet-en-podd-om-ekonomi
rss-ufobortom-rimligt-tvivel
rss-vetenskapsradion
rss-vetenskapsradion-2
rss-spraket
det-morka-psyket
svd-nyhetsartiklar
medicinvetarna
paranormalt-med-caroline-giertz
bildningspodden
sexet
hacka-livet
naturmorgon
rss-odla
barnpsykologerna
vetenskapsradion
halsorevolutionen