This talk addresses Kac’s famous question, “Can one hear the shape of a drum?”—that is, whether the spectrum of the Laplacian on a domain uniquely determines its shape— in the context of convex planar billiard tables. While non-convex counterexamples are known (Gordon–Webb–Wolpert), the problem remains open for strictly convex domains with smooth boundaries. As shown by Anderson, Melrose, and Guillemin, the spectral question is deeply connected to its dynamical analogue: whether the length spectrum—the set of lengths of all periodic billiard trajectories—determines the domain up to isometry. In joint work with Vadim Kaloshin and Alfonso Sorrentino, we show that this is indeed the case for domains that are sufficiently close to a general ellipse and possess dihedral symmetry. Note: This talk is part of the activity of the MIUR Department of Excellence Project MatMod@TOV (2023-2027)