On the minimal model program for $3$-folds in small characteristic

In this talk I will discuss recent progress on the birational geometry of algebraic varieties of dimension $3$ over an algebraically closed field of characteristic $p = 2; 3; 5$. In particular I will discuss the minimal model program for threefolds in characteristic $5$ and the birational minimal model program for $3$-folds in characteristics $2, 3$. This is joint work in progress with J. Witaszek