Date & Time: Wednesday, August 05, 2009, 16:00-17:00.
Venue: Ramanujan Hall
Title: Class Groups of Number Fields and the Cohen-Lenstra Heuristics
Speaker: Manjul Bhargava, Princeton University
Abstract: Class groups of number fields are among the most important but also most mysterious objects in algebraic number theory. Although they are just finite abelian groups, very little is understood about the structure and behavior of these groups as the number field varies.
However, there are some famous and very precise conjectures, known as the "Cohen-Lenstra-Martinet heuristics", which predict the behavior of these groups on average. In this lecture, we will describe these remarkable conjectures; we will also discuss the four or five proven cases of these conjectures, including some very recent work.