In this paper, we study the amoeba volume of a given $k$-dimensional generic analytic variety $V$ of the complex algebraic torus $(C^*)^n$. When $n>=2k$, we show that $V$ is algebraic if and only if the volume of its amoeba ...

Our understanding of algebraic representations of reductive algebraic groups in positive characteristic has seen big advances in the last years and has been largely transformed into the geometric theory of studying parity ...

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 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 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 ...

We provide new forbidden criterion for realizability of smooth tropical plane curves. This in turn provides us a complete classification of smooth tropical plane curves up to genus six.

Progress in algebraic geometry often comes through the introduction of new tools and ideas to tackle the classical problems in the development of the field. Examples include new invariants that capture some aspect of ...

Progress in algebraic geometry often comes through the introduction of new tools and ideas to tackle the classical problems the development of the field. Examples include new invariants that capture some aspect of geometry ...