704 citations · 2.4k across the 64 of their papers we have counts for
73 papers
Genericity of contracting geodesics in groups
Kunal Chawla, Inhyeok Choi, Giulio Tiozzo
Let G be a finitely generated group and Cay(G, S) be the Cayley graph of G with respect to a finite generating set S. We characterize the Gromov hyperbolicity of G in terms of the…
Equidistribution of hyperbolic groups in homogeneous spaces
Ilya Gekhtman, Samuel J. Taylor, Giulio Tiozzo
We prove that infinite orbits of Zariski dense hyperbolic groups equidistribute in homogeneous spaces, in the sense that the family of measures obtained by averaging along spheres…
The Poisson boundary of hyperbolic groups without moment conditions
Kunal Chawla, Behrang Forghani, Joshua Frisch +1
We prove that the Poisson boundary of a random walk with finite entropy on a non-elementary hyperbolic group can be identified with its hyperbolic boundary, without assuming any mo…
Metrics on trees I. The tower algorithm for interval maps
Giulio Tiozzo
We consider Milnor's "tower algorithm" in the space of piecewise monotone maps, an iterative algorithm on the space of metrics which unifies, on the one hand, Thurston's iterative…
Master Teapots and Entropy Algorithms for the Mandelbrot Set
Kathryn Lindsey, Giulio Tiozzo, Chenxi Wu
We construct an analogue of W. Thurston's "Master teapot" for each principal vein in the Mandelbrot set, and generalize geometric properties known for the corresponding object for…
A global shadow lemma and logarithm law for geometrically finite Hilbert geometries
Harrison Bray, Giulio Tiozzo
For geometrically finite group actions on hyperbolic metric spaces and under certain assumptions on the growth of parabolic subgroups, we prove a global shadow lemma for Patterson-…