We strive to bring together MATH+-researchers from a variety of applications with algebraic geometers to find and exploit algebraic structures in order to extend the scope of traditional research in modeling, simulation and optimization, and conversely to progress theory by advancing fundamental mathematics and build new bridges within mathematics.

During the past decade, computer scientists, physicists, biologists, applied mathematicians and engineers have begun to realize the potential utility of modern algebraic geometry. Internationally, there is an increasing number of activities under the headline “applied algebraic geometry" including programs at the Fields Institute 2016 and at the Simons Institute 2019. Since 2009 there is an algebraic geometry activity group of SIAM with a dedicated journal launched in 2017.

There is a lot of potential in Berlin mathematics for new connections and collaborations of algebraic geometry with other mathematical fields. In view of the breadth of applications represented in MATH+, this TES sets out to define applied algebraic geometry the Berlin way. In the spirit of the Topic Development Lab as a central part of MATH+ [. . . ] for building bridges between different fields of mathematics, the main goal of this Thematic Einstein Semester will be to foster cross-disciplinary interaction within Berlin, and to build a closeknit community which lives on after the TES is over.

At the core of the program will be three interrelated streams:

• Numerical Algebraic Geometry & Complexity,
• Curves, Arithmetic & Dynamics,
• Varieties & Convexity.