On p-torsion in class groups of number fields

Gauss famously investigated class numbers of quadratic fields, in particular characterizing the 2-divisibility of the class number for such fields. In general, it is expected that for a number field of any degree, and any rational prime p, the p-torsion part of the class group should be arbitrarily small, in a suitable sense, relative to the absolute discriminant of the field. This talk will present recent progress for both quadratic and higher degree number fields, in particular discussing recent joint work with Heath-Brown, and with Ellenberg and Wood.