Xin Zhang

Institut des Hautes Études Scientifiques


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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