Any plane rational self-map f:P^2->P^2 has an 'algebraic degree' defined to be the common degrees of its components in homogeneous coordinates. The sequence (deg f^n) always grows like a power L^n of some number L, the 'dynamical degree', which is a fundamental invariant for the dynamics of f. The dynamical degree is (in some sense) typically an integer, equal to the degree of f, and there are only countably many possibilities for its value in general. Nevertheless, I will describe joint work with Jason Bell and Mattias Jonsson in which we give a specific example where the first dynamical degree turns out to be a transcendental number. Speaker(s): Jeffrey Diller (University of Notre Dame)