nLab
Langlands program

Idea

The (classical) Langlands program is a modern extension of some ideas of Kronecker and Weber in number theory, relating automorphic forms and Galois representations?, and pioneered by Robert Langlands.

There is now a deep analogue for function fields, the geometric Langlands program pioneered by Beilinson and Drinfeld. See there for more details.

References

• Stephen Gelbart, An elementary introduction to the Langlands program, Bull. Amer. Math. Soc. (N.S.) 10 (1984), no. 2, 177–219; Edward Frenkel, Commentary on “An elementary introduction to the Langlands Program” by Steven Gelbart, Bull. Amer. Math. Soc. 48 (2011), 513-515, abstract, pdf
• the digital archive of Robert Langlands’ articles at sunsite.ubc.ca