Eva Miranda

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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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Well

Because we we need to look at evolution of systems that come associated with conservation of energy.

And this is very connected to the

uh evolution of an area.

Okay.

If I if I consider just two dimensions, then having a symplectic form is the same as having an area form.

So I'm measuring, not measuring with the lines just the length, but I'm measuring the area of my, and this is the measure I use, the area.

Okay?

And something very interesting is that when you talk about Riemann geometry

you have invariants and the most important invariant is curvature, okay?

And you could ask yourself, do you have such invariance in Riemannian geometry?

The answer is no.

You don't have any local invariance.

Locally, all symplectic manifolds are the same, and this is something that Darboux theorem uh tells us.

Okay?

So uh we need to look a little bit more close at Darbou theorem, but again.

Why do we care about symplectic geometry?

Because we are interested in conservative systems.

If we are mathematical physicists, if we are geometers, we need of ham we think of Hamiltonian systems.

And we think of Hamiltonian systems as vector fields sol solving the equation I showed.

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