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SUMMARY:Nodal sets\, Quasiconformal mappings and how to apply them to Land
 is' conjecture
DTSTART:20210416T141500
DTSTAMP:20260504T041947Z
UID:c1816c04eb1012a5734e9440ff07a87e93eae25c3fd7ab27c31807d4
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Aleksandr Logunov\, Princeton University\n\nAbstract: A
  while ago Nadirashvili proposed a beautiful idea how to attack problems o
 n zero sets of Laplace eigenfunctions using quasiconformal mappings\, aimi
 ng to estimate the length of nodal sets (zero sets of eigenfunctions) on c
 losed two-dimensional surfaces. The idea did not work out as it was planne
 d. However\, it appears to be useful in relation to Landis' Conjecture. We
  will explain how to apply the combination of quasiconformal mappings and 
 zero sets to quantitative properties of solutions to $\\Delta u + V u =0 o
 n the plane\, where $V$ is a real\, bounded function. The method reduces s
 ome questions about solutions to Shrodinger equation $\\Delta u + V u =0$ 
 on the plane to questions about harmonic functions. Based on a joint work 
 with E.Malinnikova\, N.Nadirashvili and F. Nazarov.\n 
LOCATION:https://epfl.zoom.us/j/81322439899?pwd=OU5ITEtTQmZzcVBBbmh5WUtRcW
 JKZz09
STATUS:CONFIRMED
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