### A catchier title than: Dynamics on infinite volume hyperbolic surfaces

Pure Mathematics Postgraduate Seminar

16th February 2018, 4:30 pm – 5:40 pm

Howard House, 4th Floor Seminar Room

In this talk I will: draw lots of pretty pictures, steal some of Davide's talk from a year ago about homogeneous dynamics, talk a bit about the hyperbolic half-plane, and most importantly explain how to generalize the study of lattices to the study of 'thin groups'.

Results in homogeneous dynamics, the study of dynamics in the space of lattices, have very important implications for physics, number theory, computer science, group theory.... Moreover the study of lattices on the hyperbolic half plane has far-reaching implications. As lattices can be thought of as discrete subgroups one can ask what other discrete subgroups give similar results. In this talk (after what I hope to be an extensive introduction) I will construct measures which capture the relevant dynamics for a wide class of discrete subgroups which are a generalization of lattices in hyperbolic space.

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