Université du Luxembourg

PhD Seminar at the Department of Mathematics (DMATH)

  • Main page
  • about
  • DMATH
  • Recent sessions
  • 2020
  • 2019
  • 2018
  • 2017
  • Archive
  • 2015 – 2016
  • 2014 – 2015
  • 2013 – 2014
  • 2012 – 2013
  • 2011 – 2012
  • 2010 – 2011
  • 2009 – 2010
  • 2008 – 2009
  • 03 May 2018 Massimo NOTARNICOLA, Nodal surface of Laplacian eigenfunctions on the three-torus
    Abstract

    At the end of the 18th century, Ernst Chladni, a physicist and musician, made an interesting discovery: he observed that when he excited a metal plate with the bow of his violin, he could hear sounds of different frequency. The plate was fixed only at its center, and when Chladni put some sand on it, then for each frequency a curious pattern appeared, today known as Chladni figures. Some time later, Kirchhoff pointed out that these patterns correspond to nodal sets of eigenfunctions of the biharmonic operator. In this talk, we introduce random Laplacian eigenfunctions on the three-dimensional torus, known as arithmetic random waves. More precisely, we prove a limit theorem for the nodal surface of arithmetic random waves as the eigenvalue goes to infinity.

Created by Robert Baumgarth | Last updated on 27 May 2020