Speaker: Henry Cohn, Microsoft Research and MIT
The Heisenberg uncertainty principle is a fundamental fact in harmonic analysis. It's often described in terms of quantum mechanics, but it simply amounts to a constraint on the behavior of a function and its Fourier transform. For example, a musical note cannot be sharply concentrated in both time and frequency. More generally, an uncertainty principle limits the control we can have over both a function and its Fourier transform simultaneously. In this talk, we'll examine an uncertainty principle of Bourgain, Clozel, and Kahane for signs of functions, which turns out to be connected to both sphere packing and quantum gravity.
