Edward Frenkel
speaker
2,304 appearances
1 recordings
1 series
first heard Apr 2023
last heard Apr 2023
Edward Frenkel’s voice in public audio — every appearance, attributed to the second.
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Sure.
So Langlands is a mathematician.
It's a name of a mathematician, Robert Langlands.
Canadian-born, still alive.
He was a professor at the Institute for Advanced Study that we talked about, where Einstein and Gödel and other great scientists have worked.
In fact, he used to occupy the office of Albert Einstein at the Institute for Advanced Study.
In the late 60s,
he came up with a set of ideas which captivated a lot of mathematicians, several generations of mathematicians by now, which came to be known as the Langlands Program.
And what it is about is connecting different fields of mathematics, which seem to be far away from each other.
For example, number theory, which, as the name suggests, deals with numbers, and various equations with, you know, like x squared plus y squared equals one.
And on the other side, harmonic analysis, something that any music lover can appreciate, because the sound of a symphony can be kind of decomposed into sounds of different instruments, and each of those sounds can be represented by a wave like this, like a sine function.
Those are the harmonics.
The period of a harmonic...
periods of different notes are different, they correspond to different notes and different instruments, different semitones, if you will.
they all combine together into something special, which cannot be reduced to any one of those.
So mathematically, it's the idea that you can decompose a signal as a collection, as a simultaneous oscillation of several elementary signals.
That's called harmonic analysis.
So what Langlands found is that some really difficult questions
number theory could be translated into much more easily tractable questions in harmonic analysis.
That was his initial idea.
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