Skip to main content

All Questions

Filter by
Sorted by
Tagged with
40 votes
1 answer
2k views

Implications and consequences of the recent proof of the geometric Langlands conjecture

I am a beginner in mathematical physics and geometric Langlands, having very limited knowledge in both fields so far. The proof of geometric Langlands conjecture is published a few months ago. What ...
12 votes
0 answers
2k views

Roadmap to geometric Langlands for a mathematical physics student

I am a student of both mathematics and physics, who has recently been studying string theory. My mathematics background is mostly differential geometry (principal bundles, Lie groups, etc.), although ...
16 votes
2 answers
2k views

Relationship between the TQFTs in Kapustin-Witten and Ben-Zvi-Sakellaridis-Venkatesh

In upcoming work of Ben-Zvi-Sakellaridis-Venkatesh, (see for instance these notes or this lecture) some important aspects of the Langlands correspondence are stated in the language of topological ...
11 votes
3 answers
1k views

The affine Grassmannian and the Bogomolny equations

In "Electric-Magnetic Duality and The Geometric Langlands Program", Sections 9 and 10, Kapustin and Witten describe certain convolution varieties in the affine Grassmannian (and more ...
9 votes
1 answer
435 views

Langlands dual group in math vs. Goddard-Nyuts-Olive dual group in physics

Given a group $G$, there is a so-called Langlands dual group $G^{∨}$. Given a group $G$, there is also a so-called Goddard-Nyuts-Olive dual group $G^{'}$ that relates to the magnetic charge. Are ...
18 votes
0 answers
1k views

Number Theory and Gravity

Langlands program is a web of far-reaching and influential conjectures about connections between number theory and geometry. Proposed by Robert Langlands at IAS (1967, 1970), it seeks to relate Galois ...
43 votes
7 answers
13k views

Number theory and physics

I was following some lectures by Edward Frenkel about Langlands correspondence. He was describing some analogies between number theory and theoretical physics (Mirror symmetry). At some point ( my ...
4 votes
0 answers
141 views

Langlands dual and integrable representations

Assume I successfully classified the integrable representations of a certain semi-simple Lie group $G$. Given this information, what do I know about the integrable representations of $G^\vee$, the ...
12 votes
0 answers
731 views

Any progress on Strominger-Yau and Zaslow conjecture?

In 2002 Hausel - Thaddeus interpreted SYZ conjecture in the context of Hitchin system and Langlands duality. Let briefly explain it Let $\pi : E \to Σ$ a complex vector bundle of rank $r$ and ...
16 votes
1 answer
2k views

Vector bundles, Higgs bundles and the Langlands program

This question is somewhat vaguely structured. But, I hope someone can make it more precise (or) it is indeed possible to answer it in the form that I am stating it.  Background : I recently chanced ...