The Langlands program and its connection to physics

[dx]

On wikipedia, it says that the Langlands program is a kind of "grand unified theory of mathematics." Does this program have any known connections to physics and in particular, quantum gravity?

 

[martinbn]

I don't think the Langlands program itself has any known connections to any physics. Some of the geometric Langlands program may have, but Langlands wouldn't call the geometric Langlands part of his program.

 

[mitchell porter]

Among the generalizations of number theory, one can ask about twin primes, zeta functions, etc, in the context of "function fields", which are actually algebras of polynomials (the elements of these fields are expressions like (x^2 + x + 1)/(x-1)). The Langlands version of this, "Geometric Langlands", has been studied using string theory, and using field theories descended from string theory.

There are also places where string theory touches on more conventional number theory, e.g. see Rolf Schimmrigk's work on modular forms.

 

[martinbn]

It should also be pointed that "grand unification of mathematics" shouldn't be understood as all of mathematics, just some parts of it.

 

[MathematicalPhysicist]

It should also be pointed that "grand unification of mathematics" shouldn't be understood as all of mathematics, just some parts of it.

Then why call it "grand unification"?
For the grant money perhaps?

 

[martinbn]

Then why call it "grand unification"?
For the grant money perhaps?

It was from wikipedia. I'd say why read wikipedia for things like this?

 

[suremarc]

The term “Grand Unification of Mathematics” comes from a mathematician named Edward Frenkel, I believe. On his website:

Frenkel’s research is on the interface of mathematics and quantum physics, with an emphasis on the Langlands Program, which he describes as a Grand Unified Theory of mathematics.

 

[martinbn]

The term “Grand Unification of Mathematics” comes from a mathematician named Edward Frenkel, I believe. On his website:

Well, he works on the gemetric Langlands program. Perhaps the question should be about the gemetric Langlands and physics.

 

[martinbn]

Peter Woit likes (for some reason) to blog about the geometric Langlands program. Here is his latest

https://www.math.columbia.edu/~woit/wordpress/?p=12179