Arithmetic statistics and the Cohen-Lenstra heuristics

27 June (morning) - 1 July 2016 (noon)

Organisers: Alex Bartel (Warwick), Benedict Gross (Harvard)

Scientific Scope

The area of Arithmetic Statistics is concerned with the behaviour of number theoretic objects in families. Some of the major problems in the field (such as Gauss's class number one problem) go back several centuries.

The Cohen-Lenstra heuristics were initially postulated in the early 1980s for the class groups of number fields. They offer a probabilistic model that seeks to explain numerous phenomena in the statistical behaviour of class groups.

The past ten years have seen an explosion of activity surrounding the Cohen-Lenstra heuristics. Several instances of the heuristics have been established, and more cases now seem within reach. Moreover Cohen-Lenstra type phenomena have been observed in such diverse areas of pure mathematics as elliptic curves, hyperbolic 3-manifolds, and the Jacobians of graphs.

This workshop will bring together experts on different aspects of Arithmetic Statistics and the Cohen-Lenstra Heuristics, and will offer a forum for discussions on recent developments and outstanding open problems. Those will include questions on the statistical behaviour of ray class groups, of Mordell-Weil groups of elliptic curves over number fields, and modification of the standard heuristics at bad primes. The format will be a mixture of research talks, of overview talks to allow young researchers a rapid entry into this active field, and of free time for discussion and collaboration.

Invited Participants

Manjul Bhargava
Henri Cohen
Tim Dokchitser
Cornelius Greither
Wei Ho
Daniel Kane
Jürgen Klüners
Hendrik W. Lenstra Jr.
Gunter Malle
Melanie Matchett Wood
Bjorn Poonen
Jack Thorne
Ila Varma
John Voight

Registration and further information

For information on how to register and to request funding, and further up-to-date informaton, please refer to the main conference website.

Mathematics Institute