Speaker
Elena Kim, MIT/Harvard
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.