Basmajian-type identities and Hausdorff dimension of limit sets

Basmajian-type identities and Hausdorff dimension of limit sets

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Yan Mary He, University of Chicago
Fine Hall 314

Basmajian's identity expresses the length of the boundary of a compact hyperbolic surface as a summation over the orthogeodesics on the surface. In this talk, I will introduce Basmajian-type series identities on limit sets associated to familiar complex dynamical systems. In particular, I will show how to extend Basmajian's identity to certain Schottky groups via analytic continuation. I will also discuss Basmajian-type identities for quadratic polynomials and its applications to Hausdorff dimension of Julia sets.