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SUMMARY:Aleksandr Logunov (Princeton)
DTSTART:20200527T131500Z
DTEND:20200527T141500Z
DTSTAMP:20260404T084050Z
UID:MathstatHelsinkiColloquium/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MathstatHels
 inkiColloquium/1/">Nodal sets and Quasiconformal mappings</a>\nby Aleksand
 r Logunov (Princeton) as part of Mathstat Helsinki Colloquium\n\n\nAbstrac
 t\nA while ago Nadirashvili proposed a beautiful idea how to attack proble
 ms on zero sets of Laplace eigenfunctions using quasiconformal mappings\, 
 aiming to estimate the length of nodal sets (zero sets of eigenfunctions) 
 on closed two-dimensional surfaces. The idea have not yet worked out as it
  was planned. However\, it appears to be useful for Landis' Conjecture. We
  will explain how to apply the\ncombination of quasiconformal mappings and
  zero sets to quantitative 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 $\\Delta u + V u =0$ on the plane to qu
 estions about harmonic functions.\n\nBased on a joint work with E. Malinni
 kova\, N. Nadirashvili and F. Nazarov.\n
LOCATION:https://researchseminars.org/talk/MathstatHelsinkiColloquium/1/
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