Basics on algebraic structures: rings and fiels. The complex field. Basics on linear algebra. Basics on analytic geometry.
The aim is to provide the basic theory of multinear algebra, its connections with multilinear geometry, its applications to discrete mathematics and statistics.
Polynomial rings. Algebraic and projective varieties. Spaces of tensors. Secant varieties and rank of tensors. Elements of Algebraic statistics. Computational algebraic geometry.
J. Harris. Algebraic Geometry. Springer.
Oral exam based on the knowledge of theoretica aspects and on the ability to manipulate concepts of multilinear geometry and apply them to solve specific questions.
Downloadable notes on the course are available in the web page of the teacher.