**abstract:**
Bootstrap percolation is one of the simplest cellular automata. One
of its basic variants is bootstrap percolation on a grid \([n]^d\) or lattice \(\mathbb{Z}^d\) with infection parameter r. This starts with a set \(A_0\) of *initially infected sites* (vertices); at each time step \(t = 1, 2, \ldots \) every site with at least \(r\) infected neighbours becomes infected. An infected site remain infected forever. We say that \(A_0\) *percolates* (with parameter \(r\)) if eventually all sites get infected; the *time of percolation* is the minimal \(t\) with \(A_t = V (G)\), and the *speed of percolation* is the number of vertices divided by this time.

In the talk I shall present a number of fundamental extremal and
probabilistic results on bootstrap percolation, including the fundamen-
tal results due to Aizenman, Lebowitz, Schonman, Holroyd, Benevides,
Przykucki, and others, and some of the results I have proved recently
with Balogh, Morris, Duminil-Copin, Riordan, Holmgren, Smith and
Uzzell.

Thu 6 Sep, 10:30 - 11:30, Aula Dini

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