The HADES seminar on Tuesday, December 3rd, will be at 2:00pm in Room 740.

Speaker: Elena Kim

Abstract: We consider a quantum cat map $M$ associated to a symplectic matrix $A$ acting on the torus ${\mathbb{T}}^{2n}$, a popular model in quantum chaos. The semiclassical limit of the mass of eigenfunctions of $M$ is characterized by the semiclassical measure.

For the analogous model on hyperbolic manifolds, the quantum unique ergodicity conjecture posits that the Liouville measure is the only semiclassical measure; however, the corresponding statement for quantum cat maps is known to be false. It is thus an open question to otherwise describe semiclassical measures for quantum cat maps.

In this talk, I will explain how the higher-dimensional fractal uncertainty principle of Cohen can be used to characterize the supports of semiclassical measures $\mu$, including cases where $\mu$ has full support.