For every number fieldK, there is a finite abelian group C called the

class group, which serves as an obstruction to unique factorization.

Since Gauss, number theorists have tried to understand questions such

as how often is C trivial, or how often C contains an element of fixed

order (as K varies). In the 1970's, Cohen and Lenstra observed

empirically that when the degree and signature of K is fixed, the

isomorphism class of C adheres to a natural probability distribution.

I'll discuss these Cohen-Lenstra heuristics and survey what is known,

including recent attempts to use algebraic geometry as a way of

justifying and, perhaps eventually, proving them.

Zoom link:

https://huji.zoom.us/j/87131022302?pwd=SnRwSFRDNXZ4QVFKSnJ1Wit2cjZtdz09

class group, which serves as an obstruction to unique factorization.

Since Gauss, number theorists have tried to understand questions such

as how often is C trivial, or how often C contains an element of fixed

order (as K varies). In the 1970's, Cohen and Lenstra observed

empirically that when the degree and signature of K is fixed, the

isomorphism class of C adheres to a natural probability distribution.

I'll discuss these Cohen-Lenstra heuristics and survey what is known,

including recent attempts to use algebraic geometry as a way of

justifying and, perhaps eventually, proving them.

Zoom link:

https://huji.zoom.us/j/87131022302?pwd=SnRwSFRDNXZ4QVFKSnJ1Wit2cjZtdz09

## Date:

Thu, 24/12/2020 - 16:00 to 17:15

## Location:

Zoom