Eva Miranda
speaker
1,609 appearances
1 recordings
1 series
first heard Jan 2025
last heard Jan 2025
Eva Miranda’s voice in public audio — every appearance, attributed to the second.
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Then
This is an example of integrable system.
And these integrable systems, these are called Tori manifolds, that they are very nice.
They were uh studied by many, many people in algebraic geometry.
Toryc toric varieties are very important in algebraic geometry, but also in symplectic geometry.
Because a thoric manifold is a manifold, simple manifold, which has an action of a torus, uh which is Hamiltonian.
Okay, and then the classification of thoric manifolds is described in a beautiful way.
Look, if we look at this example that you have here on the on the left, which is a sphere.
If you look at the what I call the moment man, which is the hate function, the image is just an inter.
Okay.
If I take if I go from dimension two to dimension four, I'm not going to be able to make a picture because I'm in dimension four.
I can only project.
And then I'm going to take the action, uh this action here.
This is an this is CP two, okay, which is a perfectly symplectic manifold, and I consider this action.
I cannot write C P two, but I can write the image of the moment map.
And the image of the moment map of the is a triangle.
And don't you think that it's a coincidence that that you take a very strange set I like CP two which I didn't define but it's a classical object in mathematics and you have a kind of bridge again.
Now it's the moment map, whose image is just a triangle.
And you think, isn't this magic?
Indeed there is this theorem of Dalsand which tells you that there is a correspondence between Tonic manifolds and Delsand polytop.
Showing 881–900 of 1,609 · page 45 of 81
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