Counting Minimally Ramified Global Fields

Algebraic Geometry and Number Theory Seminar

We discuss the problem of counting G-extensions of the rational numbers, and of a rational function field (over a finite filed), ramified at the smallest possible number of places, for various finite groups G. This discussion will take us on a tour through parameterizations of number fields, the quadratic large sieve, homology of configuration spaces, and permutation groups.