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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Appearances
It's just some some complicated stuff.
You can you can you can characterize this a a curvature which you can character you can define on this well, this is even before the word manifold existed, right?
On on the surface.
And then you can integrate using calculus and the integral of this cur Gaussian curvature divided by four pi is exactly equal to this topological number.
And that's incredible, right?
The fact that you you can do an integral it comes out to be an integer.
And that integer is exactly a topology.
So so this idea that Skaus related geometry to
to um to um um topology in the in this one sweep.
And then what's
What's even the next level comes Riemann.
Riemann says, Well, what you can do is to complexify
So these are no longer you know real uh uh the real connected compact orientable surfaces.
But you can think about these as complex objects.
So that so so what do we mean by that is well if you think about you know the the the real Cartesian plane, that's a two-dimensional object.
But you can
Equally think of that as a one complex dimensional object, namely the complex plane.
Yeah, the complex line, exactly.
So the with what's R2, Riemann would call C.
And then Riemann realized that you you can put similar structure on all of these things as well.
Showing 841–860 of 1,500 · page 43 of 75
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