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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
21
votes
1
answer
4k
views
What is the current status of the function fields Langlands conjectures?
My question, roughly speaking is, what happened to the function fields Langlands conjecture? I understand around 2000 (or slightly earlier perhaps), Lafforgue proved the function fields Langlands corr …
5
votes
Number Theory and Geometry/Several Complex Variables
"Higher dimensional geometry" traditionally doesn't mean this I think, so this is only partially relevant to your question (and this isn't really related to complex analysis side); if you broaden your …
1
vote
cohomology of moduli spaces
This is for Shimura varieties only; I've read only parts of the introduction so I don't know exactly what's done, but both seem to be related to $l$-adic cohomology of Shimura varieties :
Taylor & …