PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Robert Vaughan.

Title:The Uncertainty Principle and a theorem of Tao
Seminar:Algebra and Number Theory Seminar
Speaker:Ram Murty, Queen's University
Abstract:
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
Date:09 / 08 / 2011
Time:11:15am - 12:05pm