Dynamical Studies of Euclidean Minima

The Euclidean minimum is a numerical indicator that detects whether there is an Euclidean algorithm in a number field with respect to its algebraic norm. In this talk, we will briefly survey the history of its studies, in particular Cerri’s work and his algorithm for the computation of Euclidean minima. Then we will discuss how facts from dynamical systems can be applied to show computability in finite time for all fields of degree 7 or higher and to produce computational complexity bounds for most fields. The talk will be based on recent joint works with Uri Shapira, as well as on previous works with Elon Lindenstrauss.