# Generic Local $L^\infty$-Bounds for Conformal Families of Laplace Operators

 ANALYSIS/MATHEMATICAL PHYSICS SEMINAR Topic: Generic Local $L^\infty$-Bounds for Conformal Families of Laplace Operators Speaker: John Toth Affiliation: McGill University Date: Friday, January 28 Time/Room: 2:00pm - 3:00pm/S-101

Let (M,g) be a compact, closed manifold and g_u be a family of conformal metric deformations of g supported in a small ball B(\delta) of radius \delta>0. We show that for a class of such deformations, the corresponding Laplace eigenfunctions almost surely have L^\infty-bounds in B(\delta) that are consistent with random wave predictions.