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 |