Illya Koval (IST Austria)

Title: The singular support of the wave trace and the length spectrum are often non-equal near ellipses

Abstract: In this talk we explore the relation between the Laplace and the length spectra of the domain. This relation involves the wave trace - a distribution obtained from Laplace eigenvalues. The singularities of
this distribution lie within the length spectrum and arise from periodic billiard trajectories. We will describe
how one can perturb an ellipse, such that the contributions of several orbits to the wave trace
cancel out, thus making it finitely smooth. This shows that the length spectrum can be richer then the
Laplace spectrum and that it can be hard to hear the length spectrum of the drum.