For more information about this meeting, contact Robert Vaughan.
| Title: | The Uncertainty Principle and a theorem of Tao |
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| Seminar: | Algebra and Number Theory Seminar |
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| Speaker: | Ram Murty, Queen's University |
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| Abstract: |
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| 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 |
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| Date: | 09 / 08 / 2011 |
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| Time: | 11:15am - 12:05pm |
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