Elena Kim: Applying Cohen's higher dimensional fractal uncertainty principle to quantum chaos

Abstract: The fractal uncertainty principle of Cohen says that in \(\mathbb{R}^d\), a function cannot be localized to both a fractal set in physical space and a fractal set in Fourier space. We apply this uncertainty principle to study quantum chaos for hyperbolic manifolds and quantum cat maps. We characterize the support of \(\Delta\)-eigenfunctions on hyperbolic manifolds in the high frequency limit, an indicator of quantum behavior. We obtain similar results in the case of quantum cat maps, a discrete analogue.