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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So this means that when you take this function equal to constant and this gives you all these spheres that contract to zero, these spheres.
Do have a symplectic form associated to it.
So it's it's a magical world and it's bigger than symplectic geometry.
Hmm.
So
Then a natural question is how do Poisson manifolds look like?
And that's a question that you think that okay, if Poisson wrote the first Poisson bracket in eighteen oh zero or eighteen oh nine, you think this is a question that people should know the answer immediately after.
Do you know when this was proved?
Nineteen eighty-three.
And it was Alan Beinstein, the person you have here.
Uh-huh.
He's the first person to give the equivalent of this Darbu theorem for Poisson manifolds.
And the theorem it's very difficult to understand.
The theorem that Alan Beinstein proved is a theorem that tells you that a Poisson manifold locally is the product of a symplectic manifold with some transverse manifold that can be as complicated as the one of SO3.
Okay?
And in this one of SO3 you have these uh concentric spheres on this other picture, this one to be always this symplectic foliation.
And so the idea is that this is the product of a symplectic manifold with a Poisson manifold of which you know very little and you just know that it punishes at a point.
But if you if the Poisson manifold satisfies some condition here, look that I have jumped from notation to use my vector fields and nobody got very nervous about this.
And this is annotation, right?
This is a notation instead of vector fields.
Showing 661–680 of 1,609 · page 34 of 81
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