### Concentration properties of theta lifts

Heilbronn Number Theory Seminar

1st May 2019, 4:00 pm – 5:00 pm

Howard House, 4th Floor Seminar Room

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.

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