# Pure Maths Colloquium: Jim Belk

This talk is part of the Pure Maths Colloquium at the University of St Andrews. Check out our upcoming talks at http://theran.lt/pure-colloquium/.

Where: | Lecture Theatre D |

When: | Oct 11 2018 @ 16.00 |

Speaker: | Jim Belk University of St Andrews |

Title: | Rational actions of hyperbolic groups |

An action of a group on a compact metric space is rational if there is an assignment of binary addresses to points in the space for which the elements of the group act as asynchronous, finite-state automata. In this talk I will discuss the theory of rational actions and sketch a proof that any hyperbolic group acts rationally on its Gromov boundary. This gives an embedding of any hyperbolic group into the group of rational homeomorphisms of the Cantor set defined by Grigorchuk, Nekrashevych, and Suschanskii. This is joint work with Collin Bleak and Francesco Matucci.