Spectral interpretation of dynamical degrees of birational automorphisms

Dynamical degrees are important and difficult-to-study invariants of birational automorphisms of projective varieties. Using Shokurov’s b-divisors, Dang and Favre have generalized to higher dimensions the construction of Picard–Manin space, which is very important in birational geometry of surfaces. More precisely, they have constructed Banach spaces, on which any birational automorphism induces bounded linear operators whose spectral radii are equal to the dymanical degrees of the automorphism. I will discuss this construction and its application to the study of dynamical degrees.