Mathematics

Given a polynomial map $f:\mathbb{Q}\rightarrow\mathbb{Q}$, one can naturally associate to $f$ a sequence of Galois groups $G_{n,f}$ which encodes information about the dynamical properties of $f$. A precise understanding of how the structure of these groups changes as $f$ varies (for instance, among all maps of a fixed degree) would yield important results in arithmetic dynamics. In this talk we will discuss the family of groups $G_{n,f}$ in the case where $f$ has degree 2.