Algebraic Geometry is a branch of pure mathematics that deals with systems of polynomial equations and their solutions, which are called varieties. It has been extensively developed in the mathematical community, especially since the 20th century, e.g. by works of Grothendieck and Hilbert. What makes Algebraic Geometry special is that it connects many fields of mathematics, given that polynomials occur in many problems in various domains. Hence, algebraic geometry has deep conceptual connections to complex analysis, topology, and number theory, which have in turn led to the huge interest that currently exists in the mathematical community toward solving Algebraic Geometry problems.
In addition to the great theoretical developments in Algebraic Geometry, there are deep and important connections between Algebraic Geometry on the one hand, and problems in physics, biology and neuroscience on the other. The goal is to make Algebraic Geometry tools applicable to real-world problems, especially in Engineering and Neuroscience, and to translate the techniques and results that have been developed in the Algebraic Geometry community over the past two centuries to programs, tools, and methods that are easy-to-use and accessible for other scientists. The research in Applied Algebraic Geometry has interfaces with mathematical branches such as Algebra, Combinatorics and Convex Geometry, and other sciences such as phylogenetics, physics, statistics, computer science, neuroscience and reliability engineering.