SCNTD Melanie Wood
Abstract: Random groups in number theory and random integral matrices
There are certain finite abelian groups that arise from objects in number theory that are quite mysterious and of great interest, for example the class groups of imaginary quadratic number fields, or the Tate-Shafarevich group of an elliptic curve. We discuss the question of what a class group of a random imaginary quadratic number field, or the Tate-Shafarevich group of a random elliptic curve, looks like, and explain heuristics of several authors including Cohen and Lenstra, and Delaunay, for how these random groups behave. Finally we will relate the predictions of these heuristics to phenomena that can be seen and proven about random integral matrices.