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# Dr. John Toth, McGill University – Quantitative unique continuation for L 2 -restrictions of eigenfunction sequences

## October 26, 2022 @ 3:00 pm - 4:00 pm

Mode: In-person

Title: *Quantitative unique continuation for L ^{2 }-restrictions of eigenfunction sequences*

Abstract: Let (M, g) be a C ^{∞} compact, Riemannian manifold and uh ∈ C ^{∞}(M) be a sequence of L 2 -normalized Laplace eigenfunctions with (−h 2∆g − 1)uh = 0. Let H ⊂ M be a smooth hypersurface. In the terminology of Zelditch and Toth, the hypersurface H is good relative to the sequence uh if there exist constants h0(H), CH > 0 such that for all h ∈ (0, h0(H)], Z H |uh| 2 dσH ≥ e −CH/h . In the talk, I will describe some recent results (joint with Yaiza Canzani) on goodness of hypersurfaces relative to eigenfunction sequences and give some applications to nodal sets of eigenfunction sequences.