Algebra and Geometry, usually considered as abstract branches of Mathematics, can be successfully used for studying and solving problems arising in applicative scenarios, too. Among the main topics of such branches we mention logic, commutative and computational algebra, graph theory, number theory, projective and affine geometry, discrete geometry, convex geometry, integral geometry, (multivariate) complex analysis, measure theory.

The group Geometry and Algebra in Applications (GAIA) collects the members of the Mathematics Department of Politecnico of Milano that are, or have recently been, involved in applicative research projects, i.e. in research projects whose aim is to provide a solution to an applicative problem and whose team consists also of researchers from applied sciences, such as physics or engineering.