Events

Date: 3 April 2025   Time: 13:00 - 14:00     

Location: MB-503

Substitution rules provide a classical method for constructing aperiodic tilings of Euclidean space. In my talk I will describe how they may additionally generate tilings of the hyperbolic upper-half space, extending constructions previously considered by, among others, Penrose, Kakutani and Kamae (and essentially illustrated by Escher). I will illustrate results about orbits under horospheric and geodesic isometries, including a prime orbit theorem for the geodesic flow. The dynamical zeta function exhibits rich and intricate patterns of resonances, and I will discuss recent results about their locations and real projections in the special case of incommensurable alpha-Kakutani substitution rules. Based on works in progress with Alon Nishry and Yaar Solomon.