Non-random Primes: the Distribution of Class Groups by Weitong Wang
The Cohen-Lenstra-Martinet Heuristics provide us with basic ideas on the statistical results class groups of number fields. We can apply the heuristics to the Sylow subgroups of the class groups, where the choice of prime satisfies the criterion given by Cohen and Martinet, hence the name good prime. In this talk, however, I will present several examples focused on the primes that both are not good and give us statistical results like infinite moments which show fundamental difference from what a good prime could give.