Higher Dimensional Fractal Uncertainty

A fractal uncertainty principle (FUP) roughly says that a 
function and its Fourier transform cannot both be concentrated on a 
fractal set. These were introduced to harmonic analysis in order to 
prove new results in quantum chaos: if eigenfunctions on hyperbolic 
manifolds concentrated in unexpected ways, that would contradict the 
FUP. Bourgain and Dyatlov proved FUP over the real numbers, and in this 
talk I will discuss an extension to higher dimensions. The bulk of the 
work is constructing certain plurisubharmonic functions on C^n.