It was shown by C. L. Siegel (1929) that the eigenvalues of the vibrating membrane problem has no non-trivial multiplicities. In this talk we consider the eigenvalues of the vibrating clamped plate problem. This is a fourth order problem. We show that its eigenvalues
have multiplicity at most six. The proof is based on a new recursion formula for
a Bessel-like function and on Siegel-Shidlovskii Theory.
If time permits we also consider the problem of determining the density of the
nodal sets of a clamped plate.
The talk is based on joint work with Dan Mangoubi.

Zoom link: https://huji.zoom.us/j/85122089327?pwd=VFRNalFmMmdubjFrM3AwK3JZa3U5QT09