### Fine scale statistics of fractal sets

Ergodic Theory and Dynamical Systems Seminar

4th April 2019, 2:00 pm – 3:00 pm

Howard House, 4th Floor Seminar Room

Fine scale statistics of point processes have been extensively studied in

number theory and quantum chaos. Conventionally, an investigated point process

is uniformly distributed in its ambient space. Nevertheless, hyperbolic geometry

provides natural point processes that converge to fractal sets. In this talk I will

explain how to use homogeneous dynamics to study the ne scale statistics of these

point processes, such as the pair correlation of centers of circles from an Apollonian

circle packing.

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