The Enriques surface of minimal entropy

Salem numbers appear naturally as dynamical degrees of isometries of hyperbolic lattices and hence in the study of entropy of surface automorphisms. The conjecturally smallest Salem number is Lehmer's number $\lambda_{10}$, which can be realized by automorphisms of K3 surfaces and rational surfaces by work of McMullen. In this talk, I will explain how to generalize a result of Oguiso asserting the non-realizability of $\lambda_{10}$ for automorphisms of Enriques surfaces over the complex numbers to odd characteristics. Then, I will describe the unique counterexample in characteristic 2. This is joint work with Giacomo Mezzedimi and Davide Veniani.