9.30-10.30 Nicole Raulf (Lille) Asymptotics of class numbers

10.45-11.45 Christopher Frei (Graz) Constructing abelian extensions with prescribed norm

12.00-13.00 Polyxeni Spilioti (Aarhus)  A prime geodesic theorem for SL_3(Z)

​

Abstracts: 

​

​

Frei: Let K be a number field, S a finite set of elements of K, and
G a finite abelian group. We explain how to construct explicitly a
normal extension L of K with Galois group G, such that all elements of S are norms of elements of L. The construction is based on class field theory and a recent formulation of Tate’s criterion for the validity of the Hasse norm principle. This is joint work with Rodolphe Richard (UCL).

​

Raulf: We present results of the asymptotic behaviour of class numbers in the situation that the class numbers are ordered by the size of the regulator. We also will discuss the methods that

can be used to obtain these results.

​

Spilioti: 

In this talk, we will present a prime geodesic theorem for the group SL_3(Z). This is an arithmetic prime geodesic theorem for a higher rank locally symmetric space. Depending on the time, we will present a formulation of this theorem that involves class numbers.

This is a joint work with A. Deitmar and Y. Gon.

​

​