DG-categorical dynamics

We will discuss the notion of entropy in the following contexts: holomorphic, birational and DG-categorical. We will be mostly interested in the algebraicity phenomenon. In the case of a compact Kähler manifold the algebraicity follows from the Gromov–Friedland theorem. In the birational and DG-categorical case the question is still open. We will also discuss the relation with dynamical Mordell–Lang conjecture.