Algebraic Geometry in the interface of Pure and Applied Mathematics

A. DICKENSTEIN

Rio de Janeiro

Congreso; International Congress of Mathematicians 2018; 2018

International Mathematical Union

In its simplest form, algebraic geometry is the study of geometric objects defined by (typically nonlinear) algebraic equations, i.e., multivariate polynomials. Many models in the sciences and engineering are expressed as sets of real solutions to such systems of polynomial equations. Algebraic geometry is good at counting (solutions, tangencies, obstructions, etc.), giving structure to interesting sets (varieties with special properties, moduli spaces, etc.) and, principally, understanding structure. Starting in the 80´s with the development of Computer Algebra Systems (CAS), and increasingly over the last years, ideas and methods from algebraic geometry are being applied in a great number of new areas (both in mathematics and in other disciplines including biology, computer science, physics, chemistry, etc.). This article is a survey of some of these exciting developments.