Weak Weyl's Law for self-dual automorphic representations of GL_n(A_Q)

Weyl's Law provides a convenient way of counting (cuspidal) automorphic representations of GL_n(A_Q). After discussing this result, I'll focus on the number of self-dual automorphic representations. Self dual representations of GL_n play an important role in the Langlands program - they arise as functorial lifts from symplectic and orthogonal groups. I'll outline how one uses this to obtain lower and upper bounds on the number of self-dual  representations. Time permitting, I'll also talk about the local notion of depth, which plays a crucial role in the proof.