3 ms·

Wait, what? Are you claiming that mirror symmetry is "secretly" Langlands? This is not my understanding, and I'd appreciate a citation if you are indeed making

Wait, what? Are you claiming that mirror symmetry is "secretly" Langlands? This is not my understanding, and I'd appreciate a citation if you are indeed making that claim. Moreover, it does not seem to me that, for example, the Clay Millennium problems are all glosses on the same underlying problem, so I'm a bit confused by your statement.

goldenkey 5y ago
I was just linking to Langlands as another example of duality of topics in mathematics. Just like NP-complete problems are equivalent, the hardest problems in mathematics are most likely also part of some complexity class and equivalent to eachother. Take what we see here and in Langlands and generalize it to information, computation, formal languages, model theory, in general. There is probably a unified theory of "problems" that glues all the hardness together. Just my opinion..not a claim.
q-big 5y ago
> Wait, what? Are you claiming that mirror symmetry is "secretly" Langlands? There is a geometric analogue to the Langlands correspondence called "geometric Langlands correspondence": > https://en.wikipedia.org/wiki/Geometric_Langlands_correspondence https://en.wikipedia.org/wiki/Geometric_Langlands_correspond... There is a relationship beetween the geometric Langlands correspondence and S-duality > https://en.wikipedia.org/wiki/S-duality https://en.wikipedia.org/wiki/S-duality a duality that is considered in string theory. Another duality that is considered in string theory is T-duality: > https://en.wikipedia.org/wiki/T-duality https://en.wikipedia.org/wiki/T-duality The latter duality is strongly related to mirror symmetry.
- spekcular 5y ago
  Sure, but the fact that one can play "six degrees of Kevin Bacon" with Wikipedia and get from Langlands to mirror symmetry is not evidence one problem is actually the other in disguise. Already at the first link, it's unclear that resolving the usual Langlands program would say anything about geometric Langlands.
- dabed 5y ago
  I would like to read more on this, do you have any further references?

goldenkey 5y ago

I was just linking to Langlands as another example of duality of topics in mathematics. Just like NP-complete problems are equivalent, the hardest problems in mathematics are most likely also part of some complexity class and equivalent to eachother. Take what we see here and in Langlands and generalize it to information, computation, formal languages, model theory, in general. There is probably a unified theory of "problems" that glues all the hardness together. Just my opinion..not a claim.

q-big 5y ago

> Wait, what? Are you claiming that mirror symmetry is "secretly" Langlands? There is a geometric analogue to the Langlands correspondence called "geometric Langlands correspondence": > https://en.wikipedia.org/wiki/Geometric_Langlands_correspondence https://en.wikipedia.org/wiki/Geometric_Langlands_correspond... There is a relationship beetween the geometric Langlands correspondence and S-duality > https://en.wikipedia.org/wiki/S-duality https://en.wikipedia.org/wiki/S-duality a duality that is considered in string theory. Another duality that is considered in string theory is T-duality: > https://en.wikipedia.org/wiki/T-duality https://en.wikipedia.org/wiki/T-duality The latter duality is strongly related to mirror symmetry.

spekcular 5y ago
Sure, but the fact that one can play "six degrees of Kevin Bacon" with Wikipedia and get from Langlands to mirror symmetry is not evidence one problem is actually the other in disguise. Already at the first link, it's unclear that resolving the usual Langlands program would say anything about geometric Langlands.
dabed 5y ago
I would like to read more on this, do you have any further references?