Dynamics of rational self-maps (following Roland K. W. Roeder)

The dynamical degrees of a rational self-map $f$ of some algebraic variety $X$ are fundamental invariants describing the rate of growth of the action of iterates of this map on the cohomology of $X$. When $f$ has nonempty indeterminacy set, these quantities can be very difficult to determine because of non-functoriality of pullbacks under compositions of rational maps. In this talk we introduce some criterion which generalizes the criteria of Diller–Favre, Bedford–Kim, and Dinh–Sibony. We will also discuss some examples in which the dynamical degree can be calculated explicitly.