Steklov Spectral Inverse Problem in a Conformal Class

This seminar talk from the "Spectral Geometry in the clouds" series features Benjamin Florentin from Institut Elie Cartan de Lorraine discussing the Steklov spectral inverse problem within a conformal class. Explore whether it's possible to determine the shape of a "Steklov drum" from its spectrum, or equivalently, from the spectrum of its Dirichlet-to-Neumann map. The presentation examines how spectral invariants can be identified through the Duistermaat-Guillemin trace formula by studying singularities in the wave operator's trace when the boundary is Anosov with simple length spectrum. Learn how these invariants can be combined with the geodesic X-ray transform's injectivity to address the problem. Discover results obtained within the class of conformal metrics and understand how, generically, it's possible to "hear the Taylor series at the boundary" of a conformal Steklov drum.