In the beginning of 19th century Napoleon set a prize for the best mathematical explanation of Chladni’s resonance experiments. Nodal geometry studies the zeroes of solutions to elliptic differential equations such as the visible curves that appear in Chladni's nodal portraits. We will discuss geometrical and analytic methods to study zero sets of harmonic functions and eigenfunctions of the Laplace operator that allow to effectively estimate the size of the nodal sets.

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