# Colloquium abstracts

Laurent Clozel
Universite Paris-Sud, France
August 20, 2009

The Heisenberg principle and positivity:  The Heisenberg principle limits the products of the dispersions of a function and its Fourier transform. A natural problem, in particular in number theory, is to limit the product of the width of the intervals outside which $f$ and $\hat{f}$ are $>0$. We show that, as in the classical \\problem, there is a lower bound. (This is common work with J. Bourgain and J.-P. Kahane.)
I will also explain the (natural) number-theoretic motivation.