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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How do we know?

How can we choose the observables for which the bracket w works well or not?

And here comes the big, big surprise.

Let's talk about integrable systems.

Integrable systems

The name indicates something, the name indicates that you can integrate them.

Indeed, that's their origin.

But for today, it's going to be systems on a symplectic manifold.

So now we have a manifold that I told you that this is has to be even dimension dimensional with these two forms.

And I'm going to s to take a set of functions as much as n.

So half of the dimension of the manifold such that these functions poison commute.

So they have this property.

Why do I want to do this?

Because indeed, I want to find a kind of in a canonical way, a kind of position and momenta.

And I will this will be very useful to answer your question.

So I want to look at these integrable systems.

In these integrable systems, often when you take all these functions together

You call them moment map, which sounds like why do we call them moment map?

Because they are going to be like this position a momentum.

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