On a conjecture for $p$-torsion in class groups of number fields

Members' Seminar
Topic:On a conjecture for $p$-torsion in class groups of number fields
Speaker:Lillian Pierce
Affiliation:Duke University; von Neumann Fellow, School of Mathematics
Date:Monday, January 22
Time/Room:2:00pm - 3:30pm/S-101

This talk will survey ideas surrounding a conjecture in number theory about the structure of class groups of number fields. Each number field has associated to it a finite abelian group, the class group, and as long ago as Gauss, deep questions arose about the distribution of class groups as the field varies over a family. Many of these questions remain unanswered. We will introduce one particular conjecture about p-torsion in class groups, and indicate how it is closely related to several other deep conjectures in number theory. Then we will present several contrasting ways we have recently made progress toward the p-torsion conjecture.