**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.