# Questions tagged [geometric-langlands]

The geometric-langlands tag has no usage guidance.

8
questions

**40**

votes

**1**answer

10k views

### 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**

votes

**3**answers

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**

votes

**2**answers

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**

votes

**0**answers

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**

votes

**2**answers

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

**1**answer

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**

votes

**1**answer

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**

votes

**0**answers

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 ...