| 概要 | The purpose of this talk is to overview the theory of cellular automata on groups focusing on the Garden of Eden Theorem for cellular automata over amenable groups and Gottschalk's surjunctivity problem.
This includes a presentation of a few examples of cellular automata (including Conway's Game of Life) and a discussion of the notions of amenability and soficity (due to Gromov-Weiss), and of the relation between surjunctivity and Kaplansky's conjecture on stable finiteness of group rings.
The talk, completely self-contained, addresses to a wide audience, including graduate students, interested in dynamical systems, group theory, operator algebras and ring theory, and theoretical computer science. |