Counting Number Fields

A guiding question in arithmetic statistics is: Given a degree $n$ and a Galois group $G$ in $S_n$, how does the count of number fields of degree $n$ whose normal closure has Galois group $G$ grow as their discriminants tend to infinity? In this talk, I will give an overview of the history and development of number field asymptotics and we will obtain a count for dihedral quartic extensions over a fixed number field.