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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Theories of Everything with Curt Jaimungal · Eva Miranda: The Mathematical Bridge Between Classical and Quantum · 26 Jan 2025 podcast

The contraction of this vector field with a syntactic form is of one form.

So if uh if I'm a geometric, this is how I think, but this corresponds to many physical uh systems.

There's something canonical about these two forms.

This is an excellent question.

So I chose this form on purpose because if like if I'm in an if I locally, any symplectic manifold looks like that example.

This is magical.

And this works only if I'm very close to a point, right?

If I have a magnifier, I am ver looking very close to a point, then what happens if like if I'm on a Riemannian manifold, I may have change of curvature locally, and this will be an invariant, but not on a simple manifold.

So there's something very important about that.

I could think it in two ways.

Either I could think that it's

locally all simple manifolds look like that, or I could think that this is almost like a cotangent bundle.

with the with having as formed the differential of the Liubil I form.

Indeed, both things happen and you are right.

I chose I chose that in a specific way.

So this is thanks to Darbu.

Darbu proved that in that locally any simple two symplectic manifolds look exactly the same.

So I can always think that I have these uh formulas here.

I can always think that my symplectic form is as simple as that.

In a neighborhood of a point.

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