The Sarkisov program, after Hacon and McKernan

The Sarkisov program states that every birational map between Mori fiber spaces can be decomposed into a finite sequence of elementary birational transformations (so-called Sarkisov links). Following a paper by Hacon and McKernan, I will present a modern proof of this result, which is based on Shokurov’s ideas about «geography of ample models» and the results of the famous BCHM paper.