Langlands Program

The Langlands Program was proposed by Canadian mathematician Robert P. Langlands in 1967, who first proposed the concept in a letter to mathematician André Weil. The Langlands Program is a highly influential research field in modern mathematics, which involves multiple branches of mathematics such as number theory, algebraic geometry and group representation theory, and attempts to reveal the deep connections between them.

The research content of the Langlands Program is very extensive, including a series of conjectures and problems, some of which have been proved, such as the three most basic assertions of Theta correspondence, namely the Hall duality conjecture, the multiplicity conservation conjecture and the Kudla-Lalis conservation law conjecture. In addition, there is a proof of the conjecture of the multiplicity of classical groups, as well as the solution of the conservation law conjecture and the duality conjecture in the Theta correspondence theory of classical groups.