The Cohen-Lenstra heuristics has been a guiding force in research in Number Theory, specifically in the subfield of Arithmetic Statistics. These striking heuristics predict the distribution of class groups of quadratic number fields. In this talk, I will first introduce the Cohen-Lenstra heuristics and its consequences, then discuss what goes wrong at p=2. In the second part of the talk, I will discuss various ways of generalizing the Cohen-Lenstra heuristics, and its analogue in the function field case.
Talk by Ken Willyard.