# 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.