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 ...

Introduced by Bökstedt-Hsiang-Madsen in the nineties, topological cyclic homology is a manifestation of the dual visions of Connes-Tsygan and Waldhausen to extend de Rham cohomology to a noncommutative setting and to ...

Locally compact groups are ubiquitous in the study of many continuous or discrete structures across geometry, analysis and algebra. Every locally compact group is an extension of a connected group by a totally disconnected ...

The aim of this Arbeitsgemeinschaft was to understand the recent progress on Zimmer's conjecture in [1,2]. The week focuses on the cocompact case from [1].

The focus of the workshop was the connection between algebraic geometry and arithmetic. Most lectures were on p-adic topics, underlining the importance of Fontaine’s theory in the field, namely it gives a relation between ...

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, and connects with representation theory, ...

Arithmetic properties of Shimura varieties are an exciting topic which has roots in classical topics of algebraic geometry and of number theory such as modular curves and modular forms. This very active research field has ...

The theory of aperiodic order expanded and developed significantly since the discovery of quasicrystals, and continues to bring many mathematical disciplines together. The focus of this workshop was on harmonic analysis ...

The goal of this workshop was to highlight, and further, the interactions between local algebra and singularity theory. The timing was serendipitous for both subjects have witnessed tremendous progress recently, much of ...