Timeline for Need for support and guidance for my near future as a PhD student (or: has stable homotopy theory become an overly algebraic theory?)
Current License: CC BY-SA 4.0
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| Feb 27 at 19:27 | comment | added | David White | @SamHopkins For sure. But, I do think most working algebraic topologists could actually motivate the research in a way that would appeal to a layperson. For example, sometimes I talk to people about the shape of the universe, or how geometry breaks down at the event horizon of a black hole. Homotopy classes of maps are about embeddings, so one could talk about protein folding or DNA, etc. When speaking of "more than three dimensions" sometimes I mention string theory, or data sets viewed as high dimensional vectors, etc. | |
| Feb 27 at 19:12 | comment | added | Sam Hopkins | "Theory" and "application" is all relative, anyways. Many algebraic topologists will say the theoretical tools they develop are intended to help us understand the homotopy groups of spheres. I believe most mathematicians (not necessarily topologists) would find this convincing enough motivation. But of course, try explaining that an application of your work is "understanding the homotopy groups of spheres" to a random layperson and you might get a different reaction... | |
| Feb 27 at 18:44 | history | answered | David White | CC BY-SA 4.0 |