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Colloquium: Béla Bollobás
March 29, 2017 @ 12:30 pm - 1:30 pm
“A cellular automaton, introduced in the 1940s by von Neumann after a suggestion of Ulam, is an interacting particle system: a collection of sites of a lattice or a lattice-like graph, with each site in ‘state’ 0 or
‘state’ 1 (or in one of finitely many states). Starting with a certain configuration (distribution of sites), at each time-step the system updates itself according to some fixed rules: each site goes into a state that depends only on the states of a few nearby sites. Examples include the Ising model of ferromagnetism, many simple models of the brain, and Conway’s ‘Game of Life’. Despite much effort over the last fifty years, a general theory of cellular automata still seems very far out of reach.
“In my talk I shall give an introduction to a general theory of so-called monotone cellular automata on finite grids and infinite lattices when we start with a random set of sites in state 1. The foundations of this general theory were laid down only recently by Smith, Uzzell and myself; more detailed and deeper results have been obtained, among others, by Balister, Balogh, Duminil-Copin, Morris, Smith and myself.”