## PIMS/UBC Distinguished Colloquium: Béla Bollobás (Cambridge & Memphis)

- Date: 02/15/2013

Béla Bollobás, *Cambridge & Memphis*

Béla Bollobás has proved numerous important results in mathematical areas including functional analysis, combinatorics, graph theory, and percolation. He has been a Fellow of Trinity College, Cambridge since 1970 and in 2011 he was elected a Fellow of the Royal Society for his major contributions to mathematics.

University of British Columbia

Recent Results on Bootstrap Percolation.

Bootstrap percolation, one of the simplest cellular automata, can be viewed as an oversimplified model of the spread of an infection on a graph. In the past three decades, much work has been done on bootstrap percolation on finite grids of a given dimension in which the initially infected set A is obtained by selecting its vertices at random, with the same probability p, independently of all other choices. The focus has been on the critical probability, the value of p at which the probability of percolation (eventual full infection) is 1/2.

The first half of my talk will be a review of some of the fundamental results concerning critical probabilities proved by Aizenman, Lebowitz, Schonman, Cerf, Cirillo, Manzo, Holroyd and others, and by Balogh, Morris, Duminil-Copin and myself. The second half will about about the very recent results I have obtained with Holmgren, Smith, Uzzell and Balister on the time a random initial set takes to percolate.

Lecture begins at 3:00 pm in MATX 1100, preceded by a reception in MATH 125 at 2:30 pm