# IMC Colloquium Series: "Cellular Automata, a tool in pure and applied mathematics"

*Dr. Vahid Dabbaghian*

### Abstract

A cellular automata (CA) is a discrete mathematical model of spatial interactions of particular states, which changes stepwise according to specific rules conditioned on the states of neighboring cells. CA model has several applications in mathematics, physics, theoretical biology and microstructure modelling. In this talk we first review its recent application for modeling complex social systems such as, modeling HIV spread through sexual contact, modeling residential migration in response to neighborhood social dynamics, and modeling crime and the impact of liquor licensed establishment density. Then we show how linear cellular automata yields interesting patterns on elements of permutation groups, when elements are ordered by lexicographic ordering.