These lectures serve as an update of my related lectures on birational geometry in positive characteristic given in Taipei in 2013 (videos available online). In the last two years there has been lots of progress in the field especially for 3-folds for which the minimal model program has largely been established. I will discuss some of these advances assuming familiarity with the basics of the minimal model program.

 

References:

-Birkar: Existence of flips and minimal models for 3-folds in char p.

-Birkar, Waldron: Existence of Mori fibre spaces for 3-folds in char p.

-Birkar, Chen, Zhang: Iitaka's C_{n,m} conjecture for 3-folds over finite fields.