Yang-Hui He
speaker
1,500 appearances
1 recordings
1 series
first heard Jan 2025
last heard Jan 2025
Yang-Hui He’s voice in public audio — every appearance, attributed to the second.
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You get the only number two, which is a positive curvature thing.
Right.
And that's consistent with the fact that the sphere is is a positively curved object.
Locally, everywhere it's a it has positive curvature.
If you do it to a torus or or the surface of a donut, um, which is it's just called, you know, the the the the algebraic donut, you you integrate that, you get zero curvature.
And this is not a surprise because you know you have a sheet of paper, you fold it once, you get a
cylinder and you fold it again, you glue it again, you get this
This cur this um torus, this donut.
And this sheet of papers in is is inherently flat.
Right.
So if you like if you just take a piece of paper, you roll I mean like you know, you take take this piece of paper and you you roll it up, you get a you get a cylinder.
And then you do it again, and I'm not gonna you get you get the surface of a donor, like a a rubber tire.
And that is incarnate zero it's zero curvature.
And then you you can you can do this, and this is a consequence of what's known as rim Rimman uh uniformization theorem.
If you do anything that has more than one handle, you get zero curvature.
So now you have the trichotomy, right?
You get positive curvature, zero curvature, negative curvature.
The one in the middle is really obviously is interesting.
It's the boundary case.
In complex algebraic geometry, these things are called funnel varieties.
Showing 881–900 of 1,500 · page 45 of 75
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