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A New Geometry for Einstein's Theory of Relativity

(www.quantamagazine.org)
135 points jandrewrogers | 2 comments | 18 Jul 25 15:19 UTC | HN request time: 0.001s | source
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WCSTombs ◴[18 Jul 25 22:50 UTC] No.44610650[source]▶
As a one-time mathematician, this was a really fascinating article. The similarities seem to be entirely coincidental, but what would have been my doctoral dissertation was also about generalizing some concepts from smooth manifolds to a "non-smooth" setting, and the crux of my work also hinged on optimal transport.

Actually I feel optimal transport is a pretty underrated concept in both pure and applied math, and I would have loved to explore it had I continued in academia. But oh well, one must make choices in life...

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1. bmacho ◴[19 Jul 25 08:30 UTC] No.44613638[source]▶
Do I understand correctly that with sectional curvature/triangle comparison methods you can do differential geometry on non-smooth manifolds (e.g. on a cube)? If so, I've completely missed this fact before.
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2. youcandoittoo ◴[19 Jul 25 08:58 UTC] No.44613783[source]▶
Sure, see (2010) A curved Brunn-Minkowski inequality on the discrete hypercube, Or: What is the Ricci curvature of the discrete hypercube? http://www.yann-ollivier.org/rech/publs/cube.pdf

Or this: (2011) A visual introduction to Riemannian curvatures and some discrete generalizations http://www.yann-ollivier.org/rech/publs/visualcurvature.pdf

Taken from the site of Yann Ollivier http://www.yann-ollivier.org/rech/index