**D.Q. Zhang**

National University of Singapore

December 27, 2012

**Automorphisms of positive entropy on compact Kahler or algebraic varieties**:
An automorphism g on a compact variety X is of positive entropy if its action on the cohomology groups of X is of expanding type. We report recent results on the relation between the geometry of X and the existence of such expanding g and characterise those X with a maximal
number of such g of expanding type.