Seminar:
Group Actions and Dynamics
Event time:
Monday, February 28, 2022 - 4:00pm
Location:
Zoom
Speaker:
Giulio Tiozzo
Speaker affiliation:
University of Toronto
Event description:
A recurring question in the theory of random walks on groups of isometries of hyperbolic spaces asks whether the hitting (harmonic) measures can coincide with measures of geometric origin, such as the Lebesgue measure. This is also related to the inequality between entropy and drift.
We will prove that the inequality between entropy and drift is strict for certain random walks on cocompact Fuchsian groups. As we will see, this is also related to a geometric inequality for geodesic lengths, strongly reminiscent of the Anderson-Canary-Culler-Shalen inequality for free Kleinian groups.
Joint w. Petr Kosenko.