Categorical trace and the Eisenstein spectrum

This talk is about the $L^2$ space of unramified automorphic functions for a function field and its conjectural spectral decomposition over the space of Arthur parameters. I will discuss joint work with W. Reeves in which such a decomposition is established for Borel Eisenstein series. In our approach, the Arthur filtration is encoded by the theory of coherent singular support on the stack of local systems, and the passage to function theory is mediated by a categorical trace of Frobenius procedure.