Bay Area Microlocal Analysis Seminar - Landis conjecture in dimension two

Abstract: In 1960's Landis conjectured that a nontrivial solution  to a time-independent Schrödinger equation with bounded potential cannot decay faster than exponentially. In 1992 the conjecture was disproved by Meshkov, who constructed  a counter example and found the optimal rate of decay for complex valued solutions. The conjecture is still open for the case of real valued potentials. We will outline a solution in dimension two. The talk is based on a joint work in progress with A.Logunov, N.Nadirashvili and F.Nazarov.