Alternatively have a look at the program.

## Rational points on Picard modular surfaces

Picard modular surfaces X, which are smooth compactifications of the quotients Y of the complex ball by a discrete subgroups \Gamma of SU(2,1), have been studied from various points of view. They are often defined over an imaginary quadratic field M, and we are interested in the rational points of X over finite extensions k of M. In a joint work with M.

## Euler-Kronecker constants

Ihara defined and began the systematic study of the Euler-Kronecker constant

of a number field. In some cases, these constants arise in the study of periods

of Abelian varieties. For abelian number fields, they can be explicitly connected

to subtle problems about the distribution of primes. In this talk, we review some

known results and describe some joint work with Mariam Mourtada.

## Arakelov geometry, another take on L-functions

I will report on old and also not so old results relating Arakelov geometry and the theory of arithmetic L-functions.

## Hecke operators, buildings and Hall algebras

Serre's theory of trees has been applied successfully to calculations with automorphic forms for PGL(2) whenever strong approximation was sufficiently well working. This is, for instance, the case for rational function fields. In general, the class group becomes an obstruction, and a global variant of Serre's theory is needed.

## tba

## Hecke's integral formula and Kronecker's limit formula for an arbitrary extension of number fields

The classical Hecke's integral formula expresses the partial zeta function of real quadratic fields as an integral of the real analytic Eisenstein series along a certain closed geodesic on the modular curve. In this talk, we present a generalization of this formula in the case of an arbitrary extension E/F of number fields. As an application, we present the residue formula and Kronecker's limit formula for an extension E/F of number fields, which gives an integral expression of the residue and the constant term at s=1 of the``relative'' partial zeta function associated to E/F.