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Equidistribution, counting and primes for discrete groups II
Wed 27 March 2013, 11:00
Hee Oh
Brown University
Organiser: Tim Browning
ABSTRACT
[4th floor, Howard House]
In the second lecture, after giving definitions of expander family of graphs, we will discuss a recent work of Bourgain, Gamburd and Sarnak and of Salehi-Golsefidy and Varju on the expander property of the Cayley graphs of congruence family of thin hyperbolic groups and its application to sieves in linear orbits of such groups. We will then discuss
its implication on circles of prime curvature in integral Apollonian circle packings as well as a more quantitative version of the distribution of (almost) prime vectors in such orbits.