Algebraic geometry tools in systems biology

Abstract

Many models in the sciences and engineering are expressed as solution sets to systems of polynomial equations, that is, as affine algebraic varieties. This is a basic notion in algebraic geometry, a vibrant area of mathematics which is particularly 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 1980s with the development of computer algebra systems, and increasingly over the last years, ideas and methods from algebraic geometry are being applied to a great number of new areas (both in mathematics and in other disciplines including biology, computer science, physics, chemistry, etc.).