Geodesics in First Passage Percolation
  We consider a wide class of ergodic first passage percolation processes on Z^2 and prove that there exist at least four one-sided geodesics a.s. We also show that coexistence is possible with positive probability in a four color Richardson's growth model. This improves earlier results of Haggstrom and Pemantle, Garet and Marchand, and Hoffman who proved that first passage percolation has at least two geodesics and that coexistence is possible in a two color Richardson's growth model. 
Christopher Hoffman