Eduardo Martinez-Pedroza, Memorial University of Newfoundland
On Hartnell's Firefighting Problem.
The firefighter game on graphs was introduced by Bert Hartnell in 1995. Briefly, an fire breaks out at a finite set of vertices; at each time interval n ≥ 1, a fixed number of vertices p which are not on fire become protected; then the fire spreads to all unprotected neighbors of vertices on fire; once a vertex is protected or is on fire, it remains so for all time intervals. The player looks for an strategy to contain the fire. We study this game and some of its variations and show that the existence of a number p such that there is a winning strategy for any initial fire is a quasi-isometry invariant in the class of infinite graphs of bounded degree. Then we start exploring these games from geometric group theory point of view. The talk includes joint work with Danny Dyer and Brandon Thorne, and joint work with Tomasz Prytula.