Semiclassical measures of point-perturbations of the Laplacian

Point-perturbations of the Laplacian are a type of singular perturbations of the Laplacian of particular interest to the quantum chaos community in Mathematical Physics. This model was proposed to understand the transition between chaotic and integrable quantum dynamics. In this talk, we will explore this model from the Correspondence Principle, showing that on a very generic setting, high-energy eigenfunctions have invariant semiclassical measures, but on the spheres, this invariance may be broken. This talk is based on my research during my PhD studies.