Higher Dimensional Fractal Uncertainty

Alex Cohen, Massachusetts Institute of Technology
IAS - Simonyi Hall Seminar Room SH-101

This is a Joint Princeton/IAS Analysis Seminar

In-Person and Online Talk

Zoom Link: https://theias.zoom.us/j/89746906467?pwd=dGxsd1YrWkd0aWF2UEJTWFBKYUhTZz09

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.