Geb. 20.30, SR 2.058

30.01.2025

Eduard Schesler

15:45 Uhr

Abstract: In the early 1940’s the notion of a cellular automata was introduced by Stanislaw Ulam and John von Neumann and since then remained a fundamental object within and outside mathematics. Coarsely speaking, a cellular automaton over a group G and a set A (thought of as an alphabet) is a map F from the space A^G of A-valued functions on G into itself such that for each x in A^G, the value of F(x) at an element g of G only depends on a finite set of values of x. After discussing some classical examples of cellular automata, such as Conway’s game of life, we will focus on applications of cellular automata in group theory. An important result in that direction is the Garden of Eden theorem that relates the surjectivity of a cellular automaton F over an amenable group G to a weak form of injectivity of F. I will discuss how the Garden of Eden theorem can be used to characterize amenable groups. In addition, I will talk about the origin of the concept of soficity in group theory, namely Walter Gottschalk’s question whether every injective cellular automaton is surjective.