Sky Hester

In this talk, we will discuss a fundamental property of Fourier transforms,
which emerged initially in the study of the heat equation. Namely, a function
and its Fourier transform cannot both be highly localized. In this context,
we measure the concentration of a function by its differential entropy and
sketch a connection of this uncertainty principle with the Weyl-Heisenberg
inequality, which has applications in physics. We will build some context
and intuition around the Fourier transform and convolutions, as well as discuss
improvements to the bounds that appear in the entropic uncertainty
principle as it was initially proven.
Refreshments