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

And these symmetries can be encoded as group actions on the manifolds.

Today

I'm going to you know, there are going to be some group actions.

I like group actions a lot because it's a way to look at our symmetries.

No, if we have if we have a rotating object.

I you see the object rotating, but indeed this is a league group.

This is SO three.

So I like groups, I have to confess.

So in a way

uh integrable systems that are going to be important for us today are going to be a key

uh a key friend to solve the problem of choosing the observables, these integral systems, are very close to group action and to groups, to having groups.

But let's think about this simple idea from physical perspective that conserved quantities give rise to symmetries in physical systems.

So well, remember I was talking about these differential equations like three minutes ago.

We have Hamilton's equations.

This is the evolution, right, of of your system, and this system satisfies the preservation of energy, and the energy of the system usually is this Hamiltonian, which is a function, but it's the energy of your system.

Then something very, very interesting happens.

Look at this equation that I have here in uh in red.

This looks very strange.

I'm I'm contracting Omega.

Omega is a two form.

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