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 that's an example.

So if I have a symplectic manifold, I have a Poisson bracket.

And now I'm going to surprise you, Kurt, with something.

I'm going to surprise you, you're going to say, but can we define the Poisson ma bracket on a manifold that it's not symplectic?

And the answer is yes.

I'm going to give you another example.

Well, here I said Li algebras, but just think about matrices.

Okay?

I'm going to consider matrices that are traceless, so without a trace, and such that if I transpose them, they are the same as minus the matrix.

You say that's is this possible?

This set is exactly

What is called the Li algebra of SO three, okay?

But it's a set of matrices, it's an algebra, okay?

And it's an algebra because I can do the bracket.

It looks like the commutator in quantum, but now I do the bracket of matrices.

Like in the same way I would do commutators.

I do the commutator of two matrices by applying the product of two matrices and then

uh minus the product in the reverse order.

Okay?

And look what I get here.

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