Farrell Brumley

Concentration properties of theta lifts

I will present some results on the concentration properties of automorphic forms obtained through the theta correspondence. Among other things, the method relies on a distinction principle for these lifts, which detect their functorial origin via the non-vanishing of orthogonal periods. The examples we treat are in higher rank, and shed light on a purity conjecture of Sarnak. This is joint work with Simon Marshall.