This talk is based on the article by Philippe Jaming [1] concerning uncertainty principles for fractional Fourier transforms.
The article is of didactic character and presents a systematic way of generalizing any uncertainty principle for a function and its Fourier transform to an equivalent uncertainty principle for two fractional Fourier transforms, provided the associated 'angle' between the two transforms is not a multiple of π (in the classical setting, the angle is π/2).
We will go through these generalizations from the point of view of metaplectic operators and discuss what happens in higher dimensions.
[1] Jaming, P. A simple observation on the uncertainty principle for the fractional Fourier transform. J. Fourier Anal. Appl. 28, 3 (2022), Paper No. 51, 8. doi.org/10.1007/s00041-022-09946-2
https://univienna.zoom.us/j/64895816787?pwd=L0tHVnBPUkJFQVVSR3Y2QnhVRXRGZz09