June 18, 2018 12:15–13:00, Algebra, Geometry, Dynamics, and Applications. Israel Science Foundation Conference dedicated to the 90 years of Friedrich Hirzebruch. Jun. 17-22, 2018, Bar Ilan University, Ramat Gan, Israel.
Patterson-Sullivan measures for point processes and the reconstruction of harmonic functions
Abstract:
The Patterson-Sullivan construction is proved almost surely to recover every Hardy function from its values on the zero set of a Gaussian analytic function on the disk. The argument relies on the conformal invariance of the point process and the slow growth of variance for linear statistics. Patterson-Sullivan reconstruction of Hardy functions is obtained in real and complex hyperbolic spaces of arbitrary dimension, while reconstruction of continuous functions is established in general CAT(-1) spaces.
Based on joint work with Yanqi Qiu, https://arxiv.org/abs/1806.02306.