Nalini Joshi School of Mathematics and Statistics, University of Sydney Analytic Results for (Ultra-discrete) Cellular Automata Wednesday 4th October 14:05-14:55pm, Carslaw Building Room 373. Cellular automata (CA) have been widely adopted in the sciences as simple but powerful models of the real world. The complex patterns produced by their long-time behaviours are used to confirm the correctness of scientific hypotheses underlying the model. However, the analysis essential for testing scientific hypotheses appears to be missing. We show the beginnings of the mathematical analysis needed by reviewing the connection that leads from differential equations to ultra-discrete equations which are extended CA. New results for ultra-discrete equations include a test for integrability and results on solvability through associated linear problems.