we discuss various conjectures about the absolute Galois group G_Q of the field Q of rational numbers and to what extent it encodes the elementary theory of Q.
In this talk, I will introduce an internal, structural
characterisation of certain convergence properties (Fréchet-Urysohn, or
more generally, radiality) and apply this structure to understand when
Stone spaces have these properties. This work can be generalised to
certain Zariski topologies and perhaps to larger classes of spaces
obtained from other structures.
"We consider certain distinguished extensions of the field F_p((t)) of formal Laurent series over F_p, and look at questions about their model theory and Galois theory, with a particular focus on decidability."