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Thursday, October 26, 2017

**Abstract:** Montgomery and Dyson’s Pair Correlation Conjecture says that the pair correlation of the non-trivial zeros of the Riemann zeta function agrees with the pair correlation of the eigenvalues of a random Hermitian matrix. Despite its huge influence, a resolution of this conjecture seems far away. Pair correlations for some other deterministic sequences can otherwise be determined rigorously. In this talk, I will show that the limiting pair correlation of the circles from a fixed Apollonian circle packing exists. A key feature in our work, which differs from previous work in literature, is that the underlying point process is fractal in nature. A critical tool in our analysis is an extended version of a theorem of Mohammadi-Oh on the equidistribution of expanding horospheres in the frame bundles of infinite volume hyperbolic spaces. This work is motivated by an IGL project that I mentored in Spring 2017.