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### The hidden subgroup problem for infinite groups

**Algebra & Discrete Mathematics**

Speaker: | Greg Kuperberg, UC Davis |

Related Webpage: | http://www.math.ucdavis.edu/~greg/ |

Location: | Zoom lecture |

Start time: | Thu, Oct 29 2020, 10:00AM |

Given a function $f:G \to S$ on a group which is periodic with respect to a subgroup $H$, the hidden subgroup problem is the computational problem of finding $H$ from values of $f$. It is a challenge problem in quantum computing that generalizes Shor's algorithm. Shor's algorithm is the case $G = \mathbb{Z}$, finding the period of an infinite periodic sequence, and it yields among its many applications a fast quantum algorithm to factor numbers. Much of the progress on the hidden subgroup problem since Shor's stunning paper has been for finite groups. I will outline new results for this problem for infinite groups, including both hardness results and new quantum algorithms.

All meetings this quarter will be by Zoom. Please see announcements or contact organizers for the passcode. Slides for the talk are also available.

Stay afterwards for a brief, informal reception. Refreshments will be self-provided.