Questions tagged [geometric-langlands]

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Consequences of Geometric Langlands

So, lots of people work on the Geometric Langlands Conjecture, and there have been a few questions around here on it (admittedly, several of them mine). So here's another one, tagged community wiki ...
37
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3answers
3k views

Topological Langlands?

In a workshop about the geometry of $\mathbb{F}_1$ I attended recently, it came up a question related to a mysterious but "not-so-secret-anymore" seminar about... an hypothetical Topological Langlands ...
33
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2answers
5k views

Current Status on Langlands Program

The Langlands Program was launched almost fifty years ago, and progress has been made gradually, much of it hard earned. Langlands himself wrote a survey on the functoriality conjecture in 1997, Where ...
18
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0answers
830 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 ...
10
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2answers
837 views

Examples of Eigensheaves outside of langlands

In geometric Langlands, one looks at correspondences of the form $$ Bun_n(X) \leftarrow Hecke \rightarrow X\times Bun_n(X)$$ and calls a sheaf on the lefthand space Hecke eigensheaf, if pulling ...
7
votes
1answer
224 views

Beilinson-Drinfeld quantization and stable bundles

To motivate this question, I'm going to try and explain some background notions. This won't be absolutely necessary for experts, but I want to be vaguely honest about where this question comes from. ...
9
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1answer
2k views

On Geometric Langlands Correspondence

The Geometric Langlands correspondence introduced by Drinfeld and Laumon conjectures a 1 to 1 correspondence between (A) local systems on a projective smooth curve over a field and (B) (Hecke eigen-)...
7
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0answers
489 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 ...