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SUMMARY:Aleksandr Logunov (Princeton University)
DTSTART:20200609T131500Z
DTEND:20200609T141500Z
DTSTAMP:20260423T003301Z
UID:OSAnaProb/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OSAnaProb/4/
 ">Nodal sets\, quasiconformal mappings and how to apply them to Landis’ 
 conjecture</a>\nby Aleksandr Logunov (Princeton University) as part of Lei
 pzig Oberseminar Analysis - Probability\n\n\nAbstract\nA while ago Nadiras
 hvili proposed a beautiful idea how to attack problems on zero sets of Lap
 lace eigenfunctions using quasiconformal mappings\, aiming to estimate the
  length of nodal sets (zero sets of eigenfunctions) on closed two-dimensio
 nal surfaces. The idea have not yet worked out as it was planned.\n\nHowev
 er it appears to be useful for Landis' Conjecture. We will explain how to 
 apply the combination of quasiconformal mappings and zero sets to quantita
 tive properties of solutions to $\\Delta u + V u =0$ on the plane\, where 
 $V$ is a real\, bounded function. The method reduces some questions about 
 solutions to Shrodinger equation $\\Delta u + V u =0$ on the plane to ques
 tions about harmonic functions.\n\nBased on a joint work with E.Malinnikov
 a\, N.Nadirashvili and F. Nazarov.\n
LOCATION:https://researchseminars.org/talk/OSAnaProb/4/
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