### Equidistribution of generalized Farey sequences

Linfoot Number Theory Seminar

19th December 2018, 11:00 am – 12:00 pm

Howard House, 4th Floor Seminar Room

Geometrically the classical Farey sequence corresponds to an ordering of the set of cusps of the modular group when acting on hyperbolic half-space. A 'generalized Farey sequence' corresponds to the set of cusps of a different discrete subgroup of isometries. In this talk I will give a brief introduction to discrete equidistribution before showing that generalized Farey sequences equidsitribute in a natural sense in the corresponding infinite volume space. Finally I will explain how this result leads to a limiting theorem for the gap distribution and a solution to a problem in Diophantine approximation in thin groups.

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