All Questions
11 questions
9
votes
0
answers
963
views
Geometrization of the global Langlands correspondence?
Fargues-Scholze famously describe arithmetic local Langlands via global geometric Langlands on the Fargues-Fontaine (FF) curve.
The FF curve acts like an algebraic curve over $\mathbb{C}_p$ (its ...
- 15.4k
2
votes
0
answers
177
views
Why are they called reductive groups? [duplicate]
The reductive groups play a central role in the Langlands correspondence. Why are these groups called reductive? Does this name suggest something conceptual about these groups?
- 705
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 ...
- 3,309
3
votes
1
answer
607
views
Understanding moduli of shtukas of non-minuscule cocharacter
I have kind of a soft question. I've studied the basics of L. Lafforgue's proof of function field Langlands for GLn, and its use of the moduli of shtukas with two legs, and the cocharacters $[1,0,\...
- 2,044
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 ...
- 10.5k
24
votes
1
answer
3k
views
What do Hecke eigensheaves actually look like?
Let $\mathbb F_q$ be a finite field, $C$ a curve over $\mathbb F_q$ of genus $g\geq 2$, $\rho: \pi_1(C) \to GL_2(\overline{\mathbb Q}_\ell)$ an irreducible local system. The geometric Langlands ...
- 148k
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 ...
- 1,613
6
votes
1
answer
1k
views
Arthur's refinement of parameters for unitary automorphic representations
In his work on the classification of automorphic representations of a group $G$, Arthur has conjectured that the parameterization of such representations involves a homomorphism $\rho : SL_2 \times ...
- 1,073
42
votes
2
answers
8k
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 ...
- 3,799
2
votes
1
answer
753
views
Reference on Casselman-Shalika formula for GL(n) and PGL(n)?
I am looking for reference on Casselman-Shalika formula for GL(n) and PGL(n) at finite place p.
- 3,804
9
votes
3
answers
1k
views
Why is the simple trace formula a weaker tool than the Arthur trace formula?
What are some concrete examples of theorems which can be deduced from the Arthur trace formula, which do not follow from the simple trace of Kazdhan and Flicker?
(So I do not mean weaker in the sense ...
- 11.2k