Date | 2019-03-19 |
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Speaker | Diaaeldin Taha |

Dept. | Unversity of Washington |

Room | 27-325 |

Time | 16:30-17:30 |

Abstract: The Farey sequence is a famous enumeration of the rationals that permeates number theory. In the early 2000s, F. Boca, C. Cobeli, and A. Zaharescu encoded a surprisingly simple algorithm for generating--in increasing order of magnitude--the elements of each level of the Farey sequence as what grew to be known as the BCZ map, and demonstrated how that map can be used to study the statistics of subsets of the Farey fractions. In this talk, we present a generalization of the BCZ map to all Hecke triangle groups G_q, q geq 3, with the G_3 = SL(2, mathbb{Z}) case corresponding to the "classical" BCZ map. If time permits, we will present some applications of the G_q-BCZ maps to the statistics of the discrete G_q linear orbits in the plane mathbb{R}^2 (i.e. the discrete sets Lambda_q = G_q (1, 0)^T).

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