# Meeting Details

Title: The Uncertainty Principle and a theorem of Tao Algebra and Number Theory Seminar Ram Murty, Queen's University If $G$ is a finite abelian group and $f$ is a complex-valued function on $G$, the classical uncertainty principle states that for non-zero $f$, $|{\rm supp}(f)| \{\rm supp}(\hat{f})| \geq |G|$. In the case $G$ is a cyclic group of prime order $p$, Tao recently proved that $|{\rm supp}(f)| + |{\rm supp}(\hat{f})| \geq p+1$ which is a substantial improvement of the uncertainty principle. Tao's theorem hinges on a classical theorem of Chebotarev. We use the representation theory of $U(n)$ to give a new proof of the theorem of Chebotarev and thus deduce a generalization of Tao's theorem to the case of groups of prime power order. (This is joint work with J.P. Whang.)

### Room Reservation Information

Room Number: MB106 09 / 08 / 2011 11:15am - 12:05pm