The workshop brought together leading experts in Algebraic Number Theory. The talks presented new methods and results that intertwine a multitude of topics ranging from classical diophantine themes to modern arithmetic ...

Analytic number theory has florished over the past few years, and this workshop brought together world leaders and young talent to discuss developments in various branches of the subject.

The workshop on Arakelov geometry was attended by 45 participants, many of them young researchers. In 19 talks an overview of recent developments in Arakelov geometry was given.

Given a smooth projective curve $C$, nonabelian Hodge theory gives a diffeomorphism between two different moduli spaces associated to $C$. The first is the moduli space of Higgs bundles on $C$ of rank $n$, which is equipped ...

The solution to the Kadison–Singer conjecture used techniques that intersect a number of areas of mathematics. The goal of this Arbeitsgemeinschaft was to bring together people from each of these fields to support interactions ...

Arithmetic geometry is at the interface between algebraic geometry and number theory, and studies schemes over the ring of integers of number fields, or their $p$-adic completions. The talks covered a wide range of ...

The aim of this workshop was to discuss recent developments on the arithmetic of Shimura varieties and on related topics within the Langlands program, and to initiate and support further research in this direction. The ...

This meeting provided an overview of recent developments in the theory of automorphic forms and automorphic representations. In addition, new results in related areas including geometry, arithmetic geometry, moduli spaces, ...

We prove a version of Jordan's classification theorem for finite subgroups of $\mathrm{GL}_{n}(K)$ that is at the same time quantitatively explicit, CFSG-free, and valid for arbitrary $K$. This is the first proof to satisfy ...