turkmath.org

Langlands' program aims to use in_nite dimensional representations of Lie groups for the better understanding of number theory. An automorphic rep-resentation _ and its associated L-function L(s; _) are the main ingredients of the Langlands' program. This program consists of several conjectures (some of which have already been proved) which roughly state that any L-function de_ned number-theoretically can also be de_ned as an L-function of an auto-morphic representation. In Langlands' program the local and global Langlands conjectures establish a connection between the Galois representations and automorphic forms. They can be also understood as a non-abelian generalization of class _eld theory. In this talk, I will discuss local Langlands conjecture for GLn and GSp4.