This week's seminar is given by Adva Mond, University of Cambridge.
Title: The Maker-Breaker percolation game on a random board
Abstract: The (m,b) Maker-Breaker percolation game on an infinite graph G is played in the following way. Maker starts by naming a vertex v_0 as the origin. Maker and Breaker then claim respectively m and b unclaimed edges of G. Breaker wins if the component of the origin becomes finite when his edges are deleted from G. Maker wins if she can indefinitely avoid a win of Breaker.
We will discuss the state of art for this game, with special attention to the case where G is the square lattice or the result of bond percolation on it. Many interesting, and possibly accessible, open problems will be presented.
