SAXAG Algebraic Geometry initiative starts with Postdoc call

The field of algebraic geometry, which deals with the solutions of polynomial equations, dates back to the beginnings of the mathematical sciences and firm historical representation in Saxony in the form of Klein, van der Waerden, Chow, and Kähler, among others. Until the 21st century, algebraic geometry was clearly a fundamental science without direct applications.

This changed significantly with the use of computers and the development of algorithms towards more experimental methods, which led to the first applications, such as encryption systems. In particular, methods for the numerical solution of systems of polynomial equations have opened up many new fields of application, including geometric design. Data analysis and statistics are examples where geometry itself is also finding increasing applications. Algebraic manifolds of high-dimensional tensors are fundamental in computer vision and signal processing. A future focus will also lie on polynomial inequalities, which frequently occur in applications, to determine if they have real solutions.

SAXAG plans to further expand and strengthen the interface between mathematical developments and their applications outside of mathematics in Saxony. In this context, it is intended to exchange mutual expertise in particular with the disciplines of optimization, statistics, data science, image and signal processing, and in the more distant future also robotics.