In the talk we will describe some recent advances in the
geometric Langlands theory. We will introduce a new geometric
object–the stack of local systems with restricted variation and
show how it allows to formulate a version of the geometric
Langlands conjecture in any sheaf theory, in particular for
l-adic sheaves. We will then explain a procedure, given by
categorical trace, that allows that directly connect the *category*
of automorphic sheaves with the *space* of automorphic functions.