Minimal model program for threefolds in positive characteristic

Abstract: The minimal model program is supposed to help us to find a "good representative" in a given birational class. Although in characteristic 0 there has been a big progress, in positive characteristics, due to the lack of resolution of singularities and failure of vanishing theorem, things are much behind. I will talk about the recent results on the existence of flips in threefolds, jointly with Christopher Hacon, and some later improvements by Birkar and myself.